2. (i) Construct rectangle MNOP, where |MN| = 9·5 cm and |NO| = 6·5 cm .
(ii) Find the perimeter and the area of this rectangle.
3. (i)
Construct rectangle PQRS, where |PQ| = 100 mm and |QR| = 5 cm .
(ii) Find the perimeter and the area of this rectangle.
4. (i)
Construct rectangle ABCD, where | AB| = 11 cm and |BC| = 60 mm .
(ii) Find the perimeter and the area of this rectangle.
5. Find the perimeter and the area enclosed by each of the following quadrilaterals.
(i) 5 cm 3 cm (iii) 6 cm 1 cm 54 mm (v) 8.5 m 435 cm
6. Find the missing dimension ( x ) of the rectangle shown, given an area of 231 c m 2
. 23.2 Compound shapes
A compound shape is a shape that is made up from other simple shapes.
Finding the perimeter and area of a compound shape 1
Divide your shape into simple shapes (squares, rectangles, triangles). This can often be done in diff erent ways.
3 5 Add all exterior lengths to fi nd the perimeter. 2 4
By the end of this section you should be able to: ● fi nd the area and perimeter of a triangle ● fi nd the area and perimeter of compound shapes
(vi) 1 km 1 000 m (iv) 57mm (ii) 4 cm 4 cm
7. Find the missing dimension ( x ) of the rectangle shown, given an area of 480 c m 2
.
8. The rectangle on the right has an area of 65 cm ². Find the value of y.
20 cm x cm
Area 65 cm² y
9. The rectangle shown has an area of 36 cm². This rectangle has length 9 cm and width 4 cm. Write down the length and width of two other rectangles with an area of 36 cm².
9 cm length
4 cm width
10. The diagram shows a square and a rectangle. The square and rectangle have the same area. Find y .
8 cm y
11. Find the length of the side of a square, given that its perimeter is 44 cm.
12. A square has a perimeter of 31·6 cm. Find the length of a side of the square.
13. A rectangle has a perimeter of 86 cm and a width of 14 cm. Find its length.
14. A rectangle has a perimeter of 100 cm and a length of 30 cm. Find its width.
11 mm x cm
5 cm
16 cm
Work out the missing lengths around the edge of the compound shape.
Work out the area of each simple shape. Add the areas of the simple shapes together to give the total area of the compound shape.