Question

Please help

Answer 1

Answer:

Part a) $114.3\ yd^{2}$

Part b) $49.5\ yd^{2}$

Step-by-step explanation:

Part a) we know that

The area of the shaded figure is equal to the area of semicircle plus the area of a triangle

Find the area of semicircle

The area of a semicircle is equal to

$A=\frac{1}{2}\pi r^{2}$

we have

$r=5\ yd$

substitute

$A=\frac{1}{2}\pi (5)^{2}=12.5 \pi\ yd^{2}$

Find the area of triangle

The area of the triangle is equal to

$A=\frac{1}{2}(b)(h)$

we have

$b=15\ yd$

$h=5(2)=10\ yd$ -----> the height of triangle is equal to the diameter of semicircle

substitute

$A=\frac{1}{2}(15)(10)=75\ yd^{2}$

Find the area of the shaded figure

$12.5 \pi\ yd^{2}+75\ yd^{2}=(12.5 \pi+75)\ yd^{2}$

assume

$\pi=3.14$

$(12.5(3.14)+75)=114.3\ yd^{2}$

Part b) we know that

The area of the shaded figure is equal to the area of the triangle minus the area of the circle

Find the area of the circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=5\ yd$

substitute

$A=\pi (5)^{2}=25 \pi\ yd^{2}$

Find the area of triangle

The area of the triangle is equal to

$A=\frac{1}{2}(b)(h)$

we have

$b=16\ yd$

$h=16\ yd$

substitute

$A=\frac{1}{2}(16)(16)=128\ yd^{2}$

Find the area of the shaded figure

$128\ yd^{2}-25 \pi\ yd^{2}=(128-25 \pi)\ yd^{2}$

assume

$\pi=3.14$

$(128-25(3.14))=49.5\ yd^{2}$