Question

Val needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 42m​-by-42m square. Val says the area is 1005.48 m^2. Find the area enclosed by the figure. Use 3.14 for pi. What error might Val have​ made?

Thanks in advance!
I don't have anymore points so please make a good and accurate answer.

Answer 1

Area of the enclosed figure = 3148.74
`m^(2)`

Explanation:

Area enclosed by the figure = 2 x area of the semicircle + area of the square

For the semicircle,

radius =
`(diameter)/(2)`

=
`(42)/(2)`

= 21 m

area of a semicircle =
`(1)/(2)` x
`\pi r^(2)`

=
`(1)/(2)` x 3.14 x
`(21)^(2)`

= 692.37
`m^(2)`

area of a square = length x length

= 42 x 42

= 1764
`m^(2)`

Thus,

area enclosed by the figure = 2 x 692.37 + 1764

= 3148.74
`m^(2)`

The total area enclosed bu the figure is 3148.74
`m^(2)`