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snow_tiger [21]
3 years ago
12

In the figure, the radius of the partial circle with center A is 4 feet.

Mathematics
2 answers:
Aleksandr [31]3 years ago
4 0
1)24.50 ;))))))))))
2)45.68 ;)))))))))
nikdorinn [45]3 years ago
4 0

Step 1

Find the perimeter of the figure

we know that

the perimeter of a circle is equal to the circumference

C=2\pi r

where

C is the circumference of the circle

r is the radius of the circle

we have

r=4\ ft

substitute

C=2(3.14)4=25.12\ ft

In the figure

the triangle ABC is a right triangle

Applying the Pythagoras Theorem find the length side CB

CB^{2}=AB^{2} +AC^{2}

we have

AC=AB=4\ ft

substitute the values

CB^{2}=4^{2} +4^{2}

CB^{2}=32

CB=\sqrt{32}\ ft

CB=5.66\ ft

The perimeter of the figure is equal to \frac{3}{4} of the circumference plus the length side CB

so

P=\frac{3}{4}25.12+5.66=24.50\ ft

therefore

<u>the answer Part a) is </u>

the perimeter of the figure is 24.50\ ft

Step 2

Find the area of the figure

we know that

the area of a circle is equal to

A=\pi r^{2}

where

r is the radius of the circle

we have

r=4\ ft

substitute

A=3.14(4^{2})=50.24\ ft^{2}

the area of the triangle ABC is equal to

A=\frac{1}{2} bh

in this problem

b=BC=\sqrt{32}\ ft

h=BC/2=\sqrt{32}/2\ ft

substitute the values

A=\frac{1}{2}(\sqrt{32})(\sqrt{32}/2)=8\ ft^{2}

the area of the figure is equal to \frac{3}{4} of the area of the circle plus the area of the triangle ABC

A=\frac{3}{4}*50.24+8=45.68\ ft^{2}

therefore

<u>the answer Part b) is</u>

the area of the figure is 45.68\ ft^{2}

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