Question

Help please Find the area of the following colored regions?

Answer 1

Answer:

Exact Area = 36pi - 36  square meters

Approximate Area = 77.04 square meters (when using pi = 3.14)

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Explanation:

The circle has radius r = 6 meters. The area of the circle is...

A = pi*r^2

A = pi*6^2

A = 36pi

This is the exact area in terms of pi.

Because we have two right triangles, and each right triangle has the same leg length, we can effectively use the SAS theorem to prove the triangles are congruent. Therefore, both of the triangles shown have the same area. One triangle is a rotated copy of the other.

The area of one of the triangles is base*height/2 = 6*6/2 = 18 square meters. That means two of them combine to an area of 18*2 = 36 square meters.

Subtract this from the area of the circle to get the green shaded area

green area = (circle area) - (triangle areas)

green area = (36pi) - (36)

green area = 36pi - 36

This is the exact area in terms of pi. If you want the approximate area, then replace pi with its approximate value. Let's say we go for pi = 3.14

That means,

green area = 36pi - 36

green area = 36*3.14 - 36

green area = 77.04 square meters approximately

Use more decimal digits in pi to get a more accurate area value.

Answer 2

Answer:

Area = 77.1

Step-by-step explanation:

The are of a right triangle is

$\frac{1}{2} \times base \times height$

our base and height are 6 for both triangles, so we shall find the area of one of the triangles...

$\frac{1}{2} \times 6 \times 6 = 18$

multiply this by 2

$2 \times 18 = 36$

Now find the area of the whole circle

$area = \pi {r}^{2}$

our radius is 6, therefore:

$area = \pi {6}^{2} = 113.1$

Finally, subtract the area of the two triangles from the total are of the circle. The difference left over is our answer

$113.1 - 36 = 77.1$