Year 7 Shape and Geometry Worksheet - Intermediate

Year 7 Shape and Geometry worksheet for Year 7 (Key Stage 3 / Year 7-9 (Ages 11-14)). Intermediate 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)•Geometryintermediate

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Year 7 Shape and Geometry: Angles, Measures and Coordinates

Key Stage 3 | Ages 11–12 | Intermediate

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Instructions: Work through the activities in order, showing your calculations where appropriate. Use angle facts and the relevant perimeter or area formula, and include units in your answers. For coordinates, write each point as (x, y).

Angle Facts

Use the stated angle facts to find each missing angle. Show the calculation that supports your answer and include the degree symbol.

1. Angles on a straight line are 67° and x°. Find x. [2 marks]

2. Three angles around a point are 125°, 98° and y°. Find y. [2 marks]

3. Two straight lines cross. One angle is 54°. Find the vertically opposite angle. [2 marks]

4. Two angles on a straight line are (3x + 10)° and 80°. Find x. [3 marks]

Missing Angles in Triangles and Quadrilaterals

Use the angle sum of a triangle or quadrilateral to calculate each unknown. Write down the angle sum you use, then give the missing angle in degrees.

1. A triangle has angles 48°, 67° and x°. Find x. [2 marks]

2. An isosceles triangle has two equal angles of 72°. Find its third angle. [2 marks]

3. A quadrilateral has angles 85°, 110°, 95° and x°. Find x. [2 marks]

4. A quadrilateral has angles 90°, 90°, 125° and y°. Find y. [2 marks]

Perimeter and Area

Choose the correct formula for each shape. Show your working and include the appropriate units: cm for perimeter and cm² for area.

1. A rectangle is 9 cm long and 4 cm wide. Calculate its perimeter. [2 marks]

2. A rectangle is 8 cm long and 5 cm wide. Calculate its area. [2 marks]

3. A triangle has base 10 cm and perpendicular height 6 cm. Calculate its area. [2 marks]

4. A parallelogram has base 11 cm and perpendicular height 4 cm. Calculate its area. [2 marks]

5. A triangle has side lengths 7 cm, 8 cm and 9 cm. Calculate its perimeter. [2 marks]

Coordinates in All Four Quadrants

Read each coordinate pair as (x, y), with x first and y second. Give the coordinate requested, and use the signs to identify the correct quadrant where asked.

1. Point A is 3 units left of the origin and 2 units up. Write the coordinates of A. [2 marks]

2. Point B is 4 units right of the origin and 5 units down. Write the coordinates of B. [2 marks]

3. Point C has coordinates (−2, −6). Which quadrant is C in? [1 mark]

4. Point D has coordinates (5, 3). Reflect D in the x-axis and write the image coordinates. [2 marks]

Mixed Geometry Challenge

Combine the geometry skills from the earlier activities. Write a clear calculation or brief explanation for each answer, and include units where needed.

1. Three angles around a point are 145°, 120° and x°. Find x. [2 marks]

2. A triangle has angles 2x°, 3x° and 75°. Find x. [3 marks]

3. A parallelogram has base 8 cm and perpendicular height 5 cm. Calculate its area. [2 marks]

4. Point P is (−4, 3). Write the coordinates of the point 2 units to the right and 5 units down from P. [2 marks]

Answer Key

Activity 1: 113° ; 137° ; 54° ; x = 30

Activity 2: 65° ; 36° ; 70° ; 55°

Activity 3: 26 cm ; 40 cm² ; 30 cm² ; 44 cm² ; 24 cm

Activity 4: (−3, 2) ; (4, −5) ; Quadrant III ; (5, −3)

Activity 5: 95° ; x = 21 ; 40 cm² ; (−2, −2)