Area and perimeter of compound shapes · Year 7
In Area and perimeter of compound shapes (Year 7) you practise 3 skills: Compound shapes made of rectangles · Rectangles with triangles and parallelograms · Area against perimeter. A compound shape is made of several simple shapes: rectangles, triangles and parallelograms. To find its area, split it into parts, work out the area of each part, and add.
When a piece is cut out of a shape, work out the area of the whole shape and take away the area of the missing piece. For example, a triangular flower bed with a base of 4 m and a height of 3 m is cut out of a lawn 10 m by 6 m: the grass covers 60 take away 6, which is 54 m². The perimeter is the length of the edge of the shape. A side inside the shape, where two parts touch, is not part of the perimeter. Area and perimeter change in different ways. When the length of a rectangle is doubled, the area becomes twice as big, but the perimeter grows only along the two long sides. Two rectangles with the same perimeter can have different areas, too.
Tip: Before you add, check that each part is counted only once, for the area and for the perimeter.
What you learn
Compound shapes made of rectangles
For example: The lengths in the picture are in cm. What is the area of the shape, in cm²?
Answer and solution
The answer: 35 cm²
Split the shape into two rectangles, from left to right. 5 × 4 = 20 5 × 3 = 15 20 + 15 = 35 The area of the shape is 35 cm².
Rectangles with triangles and parallelograms
For example: The shape is made of a rectangle and a triangle that sits on one of its sides. The dashed line is the height of the triangle. The lengths in the picture are in metres. What is the area of the shape, in m²?
Answer and solution
The answer: 14 m²
The area of the rectangle: 4 × 2 = 8 The base of the triangle is the side of the rectangle. The area of the triangle is the base times the height, divided by 2: 4 × 3 ÷ 2 = 6 Add the areas of the rectangle and the triangle: 8 + 6 = 14 The area of the shape is 14 m².
Area against perimeter
For example: All these rectangles have a perimeter of 20 cm. Which of them has the largest area?
- 5 by 5
- 4 by 6
- 3 by 7
- 2 by 8
Answer and solution
The answer: 5 by 5
4 × 6 = 24 2 × 8 = 16 5 × 5 = 25 3 × 7 = 21 The 5 by 5 rectangle is a square, and its area is the largest: 25 cm².
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).