Question

Identify the area of the figure rounded to the nearest tenth.

Please give me a step-by-step explanation.

Answer 1

easy!

Explanation:

find the area of the rectangle and subtract the area of the semicircle.

Tip: area of semicircle is half the area of the circle.

so 22*10 is the area of the rectangle.

pi 4 squared/2

subtract the area of the semicircle from the rectangle and find the approximate total.

around 194.9

This was the way that helped me!

I got it wrong at first too, lol.

Answer 2

`A = Ar - Ac = 220cm^(2) - 50.26 cm^(2)= 169. 7 cm^(2)`

Explanation:

This problem can be solved calculating the area of the full rectangle, and substracting the area of the circle that is in the center of the figure.

The formula we use to calculate the rectangle's area is:

`Ar = b . h`

Being b = 22 cm and h= 10 cm

`Ar = 22 cm . 10 cm = 220 cm^(2)`

So now, we have to calculate the area of the circle:

`Ac = \pi . radius^(2)`

Being the radius, the half of the circle's diameter. To know the diameter (distance between opposite points of the circle), we have to substrate the space that is occupied by the circle to the full lenght of the base of the rectangle. If we know that the full lenght of the base is 22 cm, and that the opposite lenght is only 14 cm (7 cm + 7 cm), then we know that the circle occupies 8 cm (22 cm - 14 cm).

So the diameter of the circle is 8 cm. That means that it's radius is 4 cm.

`Ac = \pi . (4 cm)^(2) = \pi . 16cm^(2) = 50.26cm^(2)`

So now we substract the area of the circle to the area of the full rectangle and we obtein the area of the figure.

`A = Ar - Ac = 220cm^(2) - 50.26 cm^(2)= 169. 7 cm^(2)`

A = figure's area, Ac = circle's area, Ar= rectangle's area.