���˿���

Here is a picture of the side of a staircase. It’s called a stair stringer. Calculate the area of the side of the stringer that is facing you. Look for repeated shapes in it.

Rhys has 8 of these stringers. Each stringer needs to be coloured with wood stain twice on both sides. Calculate how much stain will be needed if a 250 ml tin will cover 40,000 cm². If this stain costs £6.95 for a 250 ml tin, how much will the stain cost?

Solution

The stringer is made up of five trapeziums, or trapezia (left), and one rectangle (right):

Let’s work out the area of one of the trapezia.

We don’t actually need the 29 cm length. It has been put in the question to confuse you.

= 26.5 × 28

= 742 cm²

Area of 5 trapezia = 742 × 5 = 3,710 cm²

Area of rectangle = 28 × 17 = 476 cm²

Total area = 3,710 + 476 = 4,186 cm²

Rhys has 8 of these stringers:

8 × 4,186 cm² = 33,488 cm²

Both sides need staining twice:

Area to be covered = 2 × 2 × 33,488 = 133,952 cm²

Number of tins required = 133,952 ÷ 40,000 = 3.3488 tins.

So we need 4 tins.

Cost of stain = £6.95 × 4 = £27.80