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27
The diagram shows a right-angled triangle and a quarter circle.
D
9 m
А
6 m
B.
The right-angled triangle ABC has angle ABC = 90°
The quarter circle has centre C and radius CB.
Work out the area of the quarter circle.
Give your answer correct to 3 significant figures.
You must show all your working.

27 The diagram shows a rightangled triangle and a quarter circle D 9 m А 6 m B The rightangled triangle ABC has angle ABC 90 The quarter circle has centre C and class=

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Answer:

A  ≈ 35.3 units²

Step-by-step explanation:

Calculate the radius CB using Pythagoras' identity in the right triangle.

CB² + AB² = AC²

CB² + 6² = 9²

CB² + 36 = 81 ( subtract 36 from both sides )

CB²  = 45 = r²

Then area of quarter circle is

A = [tex]\frac{1}{4}[/tex] × πr² = [tex]\frac{1}{4}[/tex] × π × 45 ≈ 35.3

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