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Geometry & measures topics for Secondary

Below are the Secondary topics available for the category "Geometry & measures" at Free Math Games.

These free math topics offer a complete set of basic Geometry & measures topics for Secondary pupils (Grade 7 to Grade 9, ages 11 to 14). The Geometry & measures category is divided into sub-categories such as "Circle", "Measures of 2D shapes", "Measures of 3D shapes", etc. Each sub-category has multiple sub-sub-categories, and within them are the topics with between 6 and 10 question and answer pairs for the lessons, plus additional question answer pairs for the games and tests.

For each question/answer pair in a topic you get the question as picture, equation or text, the spoken question read by a robot, and an answer as both number or text and as audio. For most topics there are also 3 wrong answers prepared for each question.

6th grade (20 topics)

Geometry & measures ➔ Circle

Geometry & measures ➔ Circle ➔ Properties

Parts of the circle 1
Identify the following parts of a circle: radius, diameter, circumference; calculate radius and diameter

Geometry & measures ➔ Measures of 2D shapes

Geometry & measures ➔ Measures of 2D shapes ➔ Perimeter

P = 2(L+W)
Perimeter of rectangles
Use the formula P=2(L+W) to calculate the perimeters of the given rectangles
P = 3L
Perimeter of triangles
Use the formula P = 3L to calculate the perimeters of each of the equilateral triangles
P = 2(B + S)
Perimeter of parallelograms
Use the formula Perimeter = 2(Base + Side) to calculate the perimeters of the given parallelograms
Perimeter of trapezia
Calculate the perimeters of the given trapezia by adding the lengths of all it's sides
Perimeter of compound shapes
Calculate the perimeters of the given compound shapes constructed from parallelograms

Geometry & measures ➔ Measures of 2D shapes ➔ Area

A = LW
Area of rectangles
Calculate the areas of the given rectangles using the formula area = length x height, A = L x W
A = BH/2
Area of triangles
Use the formula area = ½ x base x height to calculate the areas of the given equilateral triangles
A = bh
Area of parallelograms
Calculate the areas of the given parallelograms
Area of compound shapes
Calculate the areas of the given compound shapes constructed from parallelograms to 2 d.p.

Geometry & measures ➔ Measures of 3D shapes

Geometry & measures ➔ Measures of 3D shapes ➔ Volume

V = W L H
Calculate the volume of cuboids
Use the standard formula (length x width x height) to calculate the volume of cuboids

Geometry & measures ➔ Measures of 3D shapes ➔ Properties

Count edges of 3D shapes
Work out the total number of edges for each of the given solids
Count vertices of 3D shapes
Work out the total number of vertices for each of the given solids
Count faces of 3D shapes
Work out the total number of faces for each of the given solids

Geometry & measures ➔ Measures of angles

Geometry & measures ➔ Measures of angles ➔ Find the angle

Angles on a straight line
Use the angles on a straight line rule to find the missing angles
Angles around a point
Use the angles around a point rule to find the missing angles
Angles in a triangle
Use the fact that angles within a triangle sum to 180° to find the missing angles

Geometry & measures ➔ Quadrilaterals

Geometry & measures ➔ Quadrilaterals ➔ Properties

Identify the quadrilateral
Use the given properties to identify the quadrilateral
Lines of symmetry: quadrilaterals
How many lines of symmetry does each of the given shapes have?

Geometry & measures ➔ Triangles

Geometry & measures ➔ Triangles ➔ Standard conventions

Identify types of triangle
Using standard conventions identify isosceles, equilateral, right-angle and scalene triangles

7th grade (38 topics)

Geometry & measures ➔ Circle

Geometry & measures ➔ Circle ➔ Properties

Parts of the circle 2
Identify parts of the circle: arc, chord, sector, segment and tangent

Geometry & measures ➔ Measures of 2D shapes

Geometry & measures ➔ Measures of 2D shapes ➔ Perimeter

Perimeter of compound shapes
Calculate the perimeters of the given compound shapes constructed from parallelograms

Geometry & measures ➔ Measures of 2D shapes ➔ Circumference

C = 2πr
Circumference of circles
Using the formula C = 2πr calculate the circumference of circles to 2 decimal places

Geometry & measures ➔ Measures of 2D shapes ➔ Area

Area of trapezia
In each instance calculate the area of the given trapezium using the formula A = (L1 + L2)/2 x H to 2 d.p.
Area of compound shapes
Calculate the areas of the given compound shapes constructed from parallelograms to 2 d.p.
A = πr²
Area of circles
Using the formula A = πr² calculate the area of the given circles to 2 decimal places

Geometry & measures ➔ Measures of 3D shapes

Geometry & measures ➔ Measures of 3D shapes ➔ Surface area

SA = 6H²
Calculate surface area of cubes
Use multiplication or the formula SA = 6H² to calculate the surface area of cubes
SA =
2LW+2LH+2HW
Calculate surface area of cuboids
Use pairs of sides to calculate the total surface area of cuboids using the formula SA =2(LW+LH+HW)
Surface area of triangular prisms
Using a net or otherwise calculate the total surface area of triangular prisms to 2 d.p.

Geometry & measures ➔ Measures of 3D shapes ➔ Volume

V = L³
Calculate volume of cubes
Use the standard formula L³ (length cubed) to calculate the volume of cubes
V = W L H
Calculate the volume of cuboids
Use the standard formula (length x width x height) to calculate the volume of cuboids
Volume of prisms
Use the standard formula (area of cross section times length) to calculate the volume of prisms to 2 d.p.

Geometry & measures ➔ Measures of 3D shapes ➔ Properties

Count edges of 3D shapes
Work out the total number of edges for each of the given solids
Count vertices of 3D shapes
Work out the total number of vertices for each of the given solids
Count faces of 3D shapes
Work out the total number of faces for each of the given solids

Geometry & measures ➔ Measures of 3D shapes ➔ Plans and elevations

Plan view from 3-D shapes
In each instance identify the plan view from the 3-dimensional shape
Front elevation from 3-D shape
In each instance identify the front elevation of a given 3-dimensional shape
Side elevation from 3-D shape
In each instance identify the side elevation of the given 3-dimensional shape

Geometry & measures ➔ Measures of angles

Geometry & measures ➔ Measures of angles ➔ Parallel lines

Angles around parallel lines
Use parallel line rules to find alternate, corresponding and allied angles

Geometry & measures ➔ Measures of angles ➔ Find the angle

Vertically opposite angles
In each instance use vertically opposite angles to find the missing angle

Geometry & measures ➔ Measures of angles ➔ Parallel lines

Parallel lines and shapes
Use parallel line rules to find the missing angle in each of the given shapes

Geometry & measures ➔ Measures of angles ➔ Find the angle

Angles on a straight line
Use the angles on a straight line rule to find the missing angles
Angles around a point
Use the angles around a point rule to find the missing angles
Angles in a triangle
Use the fact that angles within a triangle sum to 180° to find the missing angles

Geometry & measures ➔ Polygons

Geometry & measures ➔ Polygons ➔ Properties

Identify polygons from properties
Use the given properties to identify the polygon
Lines of symmetry: polygons
Identify the number of lines of symmetry possessed by each of the given polygons
Rotational symmetry: polygons
Identify the order of rotational symmetry for each of the given polygons

Geometry & measures ➔ Polygons ➔ Interior and Exterior angles

Exterior angles of regular polygons
Use the number of sides to calculate the exterior angles for each of the given regular polygons
Number of sides from exterior angle
Use the exterior angle to calculate the number of sides for each of the given regular polygons

Geometry & measures ➔ Quadrilaterals

Geometry & measures ➔ Quadrilaterals ➔ Properties

Identify the quadrilateral
Use the given properties to identify the quadrilateral
Lines of symmetry: quadrilaterals
How many lines of symmetry does each of the given shapes have?
Rotational symmetry: quadrilaterals
Identify the order of rotational symmetry for each of the given quadrilaterals

Geometry & measures ➔ Transformations

Geometry & measures ➔ Transformations ➔ Translation

Describe translations
In each instance identify the correct column vector for the given translation
Column vectors
Identify the correct shape on the graph for the given column vector

Geometry & measures ➔ Transformations ➔ Enlargement

Negative scale factors
Identify the correct shape on the graph for the given negative scale factor enlargement
Positive integer scale factors
Identify the correct shape on the graph for the given positive integer scale factor enlargement

Geometry & measures ➔ Triangles

Geometry & measures ➔ Triangles ➔ Standard conventions

Identify types of triangle
Using standard conventions identify isosceles, equilateral, right-angle and scalene triangles

Geometry & measures ➔ Trigonometry

Geometry & measures ➔ Trigonometry ➔ SOHCAHTOA

Identify names of sides
Identify whether the marked sides of right angle triangles are the hypotenuse, adjacent or opposite

8th grade (41 topics)

Geometry & measures ➔ Circle

Geometry & measures ➔ Circle ➔ Properties

Parts of the circle 2
Identify parts of the circle: arc, chord, sector, segment and tangent

Geometry & measures ➔ Measures of 2D shapes

Geometry & measures ➔ Measures of 2D shapes ➔ Circumference

C = 2πr
Circumference of circles
Using the formula C = 2πr calculate the circumference of circles to 2 decimal places
C = πr + 2r
Circumference of semicircles
Use C = πr + 2r to calculate the circumference of the given semicircles to 2 decimal places

Geometry & measures ➔ Measures of 2D shapes ➔ Area

Area of compound shapes
Calculate the areas of the given compound shapes constructed from parallelograms to 2 d.p.
A = πr²
Area of circles
Using the formula A = πr² calculate the area of the given circles to 2 decimal places

Geometry & measures ➔ Measures of 3D shapes

Geometry & measures ➔ Measures of 3D shapes ➔ Surface area

SA = 6H²
Calculate surface area of cubes
Use multiplication or the formula SA = 6H² to calculate the surface area of cubes
SA =
2LW+2LH+2HW
Calculate surface area of cuboids
Use pairs of sides to calculate the total surface area of cuboids using the formula SA =2(LW+LH+HW)
Surface area of triangular prisms
Using a net or otherwise calculate the total surface area of triangular prisms to 2 d.p.

Geometry & measures ➔ Measures of 3D shapes ➔ Volume

V = L³
Calculate volume of cubes
Use the standard formula L³ (length cubed) to calculate the volume of cubes
Volume of prisms
Use the standard formula (area of cross section times length) to calculate the volume of prisms to 2 d.p.
V = π r² L
Calculate the volume of cylinders
Use the standard formula (area of cross section times length) to calculate the volume of cylinders to 2 d.p.

Geometry & measures ➔ Measures of angles

Geometry & measures ➔ Measures of angles ➔ Bearings

Describe the bearing
In each instance identify if the type of bearing is acute, obtuse or reflex
Estimate the bearing
Choose the most appropriate three figure bearing from the given options

Geometry & measures ➔ Measures of angles ➔ Parallel lines

Angles around parallel lines
Use parallel line rules to find alternate, corresponding and allied angles

Geometry & measures ➔ Measures of angles ➔ Find the angle

Vertically opposite angles
In each instance use vertically opposite angles to find the missing angle

Geometry & measures ➔ Measures of angles ➔ Parallel lines

Parallel lines and shapes
Use parallel line rules to find the missing angle in each of the given shapes

Geometry & measures ➔ Polygons

Geometry & measures ➔ Polygons ➔ Properties

Identify polygons from properties
Use the given properties to identify the polygon
Lines of symmetry: polygons
Identify the number of lines of symmetry possessed by each of the given polygons
Rotational symmetry: polygons
Identify the order of rotational symmetry for each of the given polygons

Geometry & measures ➔ Polygons ➔ Interior and Exterior angles

Exterior angles of regular polygons
Use the number of sides to calculate the exterior angles for each of the given regular polygons
Number of sides from exterior angle
Use the exterior angle to calculate the number of sides for each of the given regular polygons
Interior angle from exterior angle
Use the exterior angle for each regular polygon to calculate the interior angle
Sum of interior angles
Calculate the sum of the interior angles for each of the given polygons

Geometry & measures ➔ Pythagoras

Geometry & measures ➔ Pythagoras ➔ Pythagoras: 2D

Calculate the hypotenuse
Use Pythagoras' theorem to calculate the hypotenuse for these right-angle triangles to 2 decimal places
Find the missing length
Use Pythagoras' theorem to calculate the length of a side that is not the hypotenuse to 2 decimal places

Geometry & measures ➔ Quadrilaterals

Geometry & measures ➔ Quadrilaterals ➔ Properties

Rotational symmetry: quadrilaterals
Identify the order of rotational symmetry for each of the given quadrilaterals

Geometry & measures ➔ Similar shapes

Geometry & measures ➔ Similar shapes ➔ Similar shapes

Identify similar shapes
Identify the pairs of shapes which are similar

Geometry & measures ➔ Similar shapes ➔ Scale factors

Triangles: scale factors
In each instance find the scale factor between the two similar triangles
Triangles: length from scale factors
Use scale factor ratios to work out lengths on the smaller or larger of the given triangles
Other shapes: length from scale factor
Find and use the scale factor to work out lengths on similar shapes that are not triangles

Geometry & measures ➔ Transformations

Geometry & measures ➔ Transformations ➔ Reflection

Identify reflections
Identify the correct shape for the described reflection

Geometry & measures ➔ Transformations ➔ Rotation

Rotation
Identify the correct shape on the grid for the described rotation

Geometry & measures ➔ Transformations ➔ Translation

Describe translations
In each instance identify the correct column vector for the given translation
Column vectors
Identify the correct shape on the graph for the given column vector

Geometry & measures ➔ Transformations ➔ Reflection

Describe reflections
Identify the line of symmetry (also called the mirror line) for each of the reflections

Geometry & measures ➔ Transformations ➔ Rotation

Describe rotation
In each instance identify the correct description for the given rotation

Geometry & measures ➔ Transformations ➔ Enlargement

Negative scale factors
Identify the correct shape on the graph for the given negative scale factor enlargement
Positive integer scale factors
Identify the correct shape on the graph for the given positive integer scale factor enlargement

Geometry & measures ➔ Triangles

Geometry & measures ➔ Triangles ➔ Standard conventions

Identify congruent, similar triangles
Identify triangles which are congruent, similar or neither
Labels for sides, angles
Identify the standard conventions for labeling the angles and sides of different types of triangles

Geometry & measures ➔ Trigonometry

Geometry & measures ➔ Trigonometry ➔ SOHCAHTOA

Identify names of sides
Identify whether the marked sides of right angle triangles are the hypotenuse, adjacent or opposite

In addition to the Geometry & measures topics shown above, the secondary section of Free Math Games has 4 other top level categories of topics to choose from. Each top level category offers a full breadth of topics to cover the secondary curriculum. Use these topics to reinforce key math concepts in a fun and engaging way that will keep your pupils enthused and energised with the math they are learning. The top level categories available are:

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