Question

This composite figure is created by placing a sector of a circle on a rectangle. What is the area of this composite figure? Use 3.14 for pi. Show your work.

Answer 1

Answer:

area of rectangle: 64.4

area of sector: 8.3

Step-by-step explanation:

area of rectangle: 7 × 9.2 = 64.4

area of sector:

radius = 9.2 ÷ 2 = 4.6

area of circle: 3.14 × 4.6² = 66.4

66.4 × $\frac{1}{8}$ = 8.3

Answer 2

The area of the considered composite figure is 97.6212 cm²

How to find the area of a composite figure?

A composite figure is formed by composition of more than one figure. If there is no positive intersection of the figures' area, then the area of the composite figure is the sum of the areas of the composite figures.

How to find the area of a sector of a circle?

Sector of a circle is like slice of a circular pizza. Its two straight edge's having an angle, and edge's length(the radius of the circle) are two needed factors for finding the area of that sector.

Since the whole circle with radius 'r' units have 360 degrees angle on center of the circle, and its area is $\pi r^2 \: \rm unit^2$, thus, as the angle lessens, this area gets lessened.

360 degree =>  $\pi r^2 \: \rm unit^2$ area

1 degree =>  $\pi r^2 \: \rm unit^2$/360 area

x degree =>$\dfrac{x \times \pi r^2}{360} \: \rm unit^2$ area

Thus, area of a sector with edge length 'r' units and interior angle 'x' degrees is given as:

$A = \dfrac{x \times \pi r^2}{360} \: \rm unit^2$

For the given case, the composite figure is made up of two parts, one is sector of a circle with radius of 9.2 cm with angle 45 degrees, and a rectangle of dimensions 7 cm by 9.2 cm.

• Area of composite figure = Area of sector + Area of rectangle

The edge length of the sector is 9.2 cm, and the angle the sector has got is 45 degrees internally (on the side whose area is needed, and not outward angle).

Thus, we get:

Area of sector = $\dfrac{45 \times \pi \times (9.2)^2}{360} \approx 33.2212\:\rm cm^2$

And area of rectangle is its length times width = $7 \times 9.2 = 64.4 \: \rm cm^2$

Thus, the area of the composite figure is evaluated as:

Area of composite figure = Area of sector + Area of rectangle

A ≈ 33.2212 + 64.4 sq. cm  = 97.6212 sq. cm

Thus, the area of the considered composite figure is 97.6212 cm²

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