Question

PLEASE HELP

A circular garden will have grass planted around a triangular region of flowers as shown in the diagram below. How many square feet will be covered in grass? Round to the nearest square foot.


1,858 ft 2
9,888 ft 2
1,291 ft 2
1,966 ft 2

Answer 1

Option (4)

Explanation:

From the picture attached,

ΔABC is a right triangle.

Since, inscribed angle in a semicircle is always a right angle, Hypotenuse AC will be the diameter of the circle.

Length of diameter AC = 58 ft

Radius of the circle =
`(58)/(2)=29` ft

Area of the circular garden = πr² [r = radius of the circle]

= π(29)²

= 2642.08 ft²

Area of the right triangle =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(27)(50)`

= 675 ft²

Area of the of the region covered with grass = Area of the circular garden - Area of the right triangle

= 2642.08 - 675

= 1967.08 ft²

≈ 1966 [Nearest value]

Option (4) will be the answer.