Question 14b

Kendra places the figure with 2 similar triangles to form a rectangle. Find the area of the rectangle. (2 marks)

$Question 14b diagram$

Answer: 435 cm²

Workings

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parallelogram has equal opposite sides like a rectangle

let L be length of Figure 1

figure 1 perimeter → 48cm

2L + 2AB = 48cm

we can divide by 2

1L + 1AB = 48 ÷ 2 = 24 cm

figure 2 perimer = 76 cm

6L + 2AB = 76

we can divide by 2

3L + 1AB = 76 ÷ 2 = 38 1L + 1AB = 24 cm

we can minus this 2 equations

2L = 38 - 24 = 14 1L = 14 ÷ 2 = 7

length of rectangle → 8 + 3 x 7 = 29 cm

area of rectangle → 15 x 29 = 435 cm²

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