The diagram shows a shape made from a quarter circle of radius 6 cm and a right-angled triangle with a hypotenuse of length 9 cm. Which of the following expressions gives the area, in square centimetres, of the shape?

Answer:

24) C

Area of the quarter of circle = 0.25 π r²

0.25π(6)²
0.25 π 36
9π

In order to find the area of the triangle, we first need to find the base (B). We need to use Pythagoras for this. 

(9)² = (6)² + (B)²
81 = 36 + B²
45 = B²
B = √45 = √(3 x 3 x 5) = 3√5

Area of triangle = 0.5 x 6 x 3√5 = 3 x 3√5 = 9√5

Total area of shape = 9π + 9√5