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What is the area of this figure? Please show your work.

What is the area of this figure? Please show your work.-example-1
User HandMadeOX
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1 Answer

5 votes

Answer:

112.13 square mm

Explanation:

Decompose the composite figure into familiar shapes. One such decomposition is shown in the attached figure

There are four familiar shapes

A semicircle and 3 rectangles

The diameter of the semicircle = 6 mm and therefore its radius is 3mm

Area of the semicircle = 1/2 x area of circle = 1/2 x π x 3²
= 1/2 x 3.14 x 9
= 14.13 square mm

The rectangle below the semi circle has height 5 mm and width 10 mm
Area of this rectangle= 5 x 10 = 50 square mm

The rectangle at the bottom left has width = 6 mm and height = 7mm
Area of this rectangle = 6 x 7 = 42 square mm

The bottom right rectangle has width 2 mm and height 3 mm
Area of this rectangle = 2 x 3 = 6 square mm

Area of the three rectangles = 50 + 42 + 6 = 98 square mm

Total area of composite figure

= Area of 3 rectangles + Area of semicircle

= 98 + 14.13

= 112.13 square mm

What is the area of this figure? Please show your work.-example-1
User Tjwallace
by
7.4k points