Get the answers you've been searching for with IDNLearn.com. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.

4. Look at the composite figure below. A vertex of the square is the center of the circle. The side
length of the square and the radius of the circle is 8 units. To the nearest whole unit, what is the
area of the figure?
8 units
F 265 square units
G66 square units
H 215 square units
J 128 square units
EKSING TOWARD STAAR © 2014
Page


Sagot :

Answer:

Approximately [tex]215[/tex] square units.

Step-by-step explanation:

The area of this figure is equal to:

[tex]\begin{aligned}& \text{Area of figure} \\ =\; & \text{Area of square} \\ &+ \text{Area of circle} \\ &- \text{Area of overlap}\end{aligned}[/tex].

The area of the square is [tex]8^{2} = 64[/tex] square units.

The area of the circle of radius [tex]r = 8[/tex] is [tex]\pi\, r^{2} = 8^{2}\, \pi = 64\, \pi[/tex] square units.

Refer to the diagram attached. In this figure, the overlap between the square and the circle is a sector of radius [tex]r= 8[/tex]. The angle of this sector is [tex]90^{\circ}[/tex]- same as the measure of the interior angle of the square.

The area of this sector would then be:

[tex]\begin{aligned} & \pi\, r^{2} \times \frac{90^{\circ}}{360^{\circ}} = 16\, \pi \end{aligned}[/tex].

Therefore, the area of the figure would be:

[tex]\begin{aligned}& \text{Area of figure} \\ =\; & \text{Area of square} \\ &+ \text{Area of circle} \\ &- \text{Area of overlap} \\ =\; & 64 + 64\, \pi - 16\, \pi \\ \approx\; & 215 \end{aligned}[/tex].

View image Jacob193