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NeTakaya
3 years ago
11

Just tell me the steps, not the answer please. This diagram shows the aerial view of a playground. What is the area of the playg

round to the nearest square yard? Use the value = 3.14.

Mathematics
1 answer:
Oxana [17]3 years ago
5 0

Area of the circle = π * (35 yd)^2

Let <em>A</em> be the area of the sector subtended by a central angle measuring 80º. Then

<em>A</em> / (π * (35 yd)^2) = 80º / 360º  ==>  <em>A</em> = 2450π/9 yd^2 ≈ 854.78 yd^2

Subtract from <em>A</em> the area of the triangle, whose base has length 45 yd and with height 25 yd:

<em>A</em> - 1/2 * (45 yd) * (25 yd)  ≈ 292.28 yd^2

This is the area of the missing circular segment.

Then the area of the playground is equal to the area of the circle minus this area,

π * (35 yd)^2 - 292.28 yd^2 ≈ 3554 yd^2

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