Area of Composite Shapes

Try This Revisited 2

The mirror shown is in the shape of a regular octagon. The width of the mirror between the outer edges of the frame is $99$ cm.

The mirror's glass is the same size as the outer edges of the frame. What is the area of the glass?

Solution

Example 4 — Part 1

A track surrounds a grass field. The perimeter of the grass is composed of two straight sides that are each $84.39$ m long and two semicircles with radius $36.5$ m. The track is composed of lanes with a total width $10.36$ m. Installation of special rubber material for the track surface costs $$48$/m². Determine the total cost to install the track surface.

Solution — Part 1 (Area of the Grass)

The outer edge of the track and the outer edge of the grass are similar shapes. Each area is a rectangle with two half circles.

Example 4 — Part 2

A track surrounds a grass field. The perimeter of the grass is composed of two straight sides that are each $84.39$ m long and two semicircles with radius $36.5$ m. The track is composed of lanes with a total width $10.36$ m. Installation of special rubber material for the track surface costs $$48$/m². Determine the total cost to install the track surface.

Solution — Part 2 (Area of the Track and Grass)

Example 4 — Part 3

A track surrounds a grass field. The perimeter of the grass is composed of two straight sides that are each $84.39$ m long and two semicircles with radius $36.5$ m. The track is composed of lanes with a total width $10.36$ m. Installation of special rubber material for the track surface costs $$48$/m². Determine the total cost to install the track surface.

Solution — Part 3 (Total Cost)

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Area of Composite Shapes

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Try This Revisited 2

Solution

Example 4 — Part 1

Solution — Part 1 (Area of the Grass)

Example 4 — Part 2

Solution — Part 2 (Area of the Track and Grass)

Example 4 — Part 3

Solution — Part 3 (Total Cost)

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