Year 7 Shape and Geometry Worksheet - Beginner

Year 7 Shape and Geometry worksheet for Year 7 (Key Stage 3 / Year 7-9 (Ages 11-14)). Beginner level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Geometrybeginner

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Year 7 Shape and Geometry: Angles, Measures and Coordinates

Key Stage 3 • Ages 11–12 • Beginner

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Instructions: Work through the activities in order, showing your calculations where you can. Use the angle facts and formulae given in the guidance, include units for perimeter and area, and remember that coordinates are written (x, y).

Angle Facts: Lines and a Point

Angles on a straight line add to 180°. Angles around a point add to 360°, and vertically opposite angles are equal. Subtract the known angle or angles from the relevant total to find each answer.

1. Two angles on a straight line are 68° and x°. Find x.

2. Three angles around a point are 95°, 120° and y°. Find y.

3. Two straight lines cross. One angle is 47°. Find the vertically opposite angle.

4. Two angles on a straight line are (x + 20)° and 70°. Find x.

Missing Angles in Triangles and Quadrilaterals

The interior angles of a triangle add to 180°. The interior angles of a quadrilateral add to 360°. Add the angles you know, then subtract their total from the relevant angle sum.

1. A triangle has angles 55°, 65° and x°. Find x.

2. A triangle has angles 90°, 38° and y°. Find y.

3. A quadrilateral has angles 90°, 85°, 110° and z°. Find z.

4. A quadrilateral has angles 75°, 105°, 95° and w°. Find w.

Rectangle Perimeter and Area

For a rectangle, perimeter = 2 × (length + width), and area = length × width. Perimeter is measured in units such as cm; area is measured in square units such as cm². Work out both for each rectangle.

1. A rectangle is 8 cm long and 3 cm wide. Find its perimeter and area.

2. A rectangle is 9 m long and 4 m wide. Find its perimeter and area.

3. A rectangle has length 7 cm and width 5 cm. Find its perimeter and area.

Triangle and Parallelogram Measures

For a triangle, area = (base × perpendicular height) ÷ 2. For a parallelogram, area = base × perpendicular height. For perimeter, add the lengths of all the outside sides. Heights are perpendicular to the base.

1. A triangle has base 10 cm, perpendicular height 4 cm, and other sides 6 cm and 8 cm. Find its area and perimeter.

2. A triangle has base 8 m, perpendicular height 5 m, and other sides 6 m and 7 m. Find its area and perimeter.

3. A parallelogram has base 9 cm, perpendicular height 4 cm and sloping side 5 cm. Find its area and perimeter.

4. A parallelogram has base 7 m, perpendicular height 3 m and sloping side 4 m. Find its area and perimeter.

Coordinates in All Four Quadrants

Coordinates are written (x, y): move horizontally first, then vertically. Positive x is to the right and negative x is to the left; positive y is up and negative y is down. Write each point as an ordered pair.

1. Start at the origin. Move 3 units right and 2 units up. Write the coordinates.

2. Start at the origin. Move 4 units left and 1 unit up. Write the coordinates.

3. Start at the origin. Move 2 units left and 5 units down. Write the coordinates.

4. Start at the origin. Move 6 units right and 3 units down. Write the coordinates.

Answer Key

Activity 1: 112° ; 145° ; 47° ; x = 90°

Activity 2: 60° ; 52° ; 75° ; 85°

Activity 3: 1. Perimeter 22 cm, area 24 cm² ; 2. Perimeter 26 m, area 36 m² ; 3. Perimeter 24 cm, area 35 cm²

Activity 4: 1. Area 20 cm², perimeter 24 cm ; 2. Area 20 m², perimeter 21 m ; 3. Area 36 cm², perimeter 28 cm ; 4. Area 21 m², perimeter 22 m

Activity 5: (3, 2) ; (-4, 1) ; (-2, -5) ; (6, -3)