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Find the area of the regular polygon.

Round to the nearest tenth.

7 yd

[? ] yd?

1 Answer

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Answer:

98 yd²

Explanation:

From the diagram attached, The polygon is a square with the distance from the edge of the square to the center of the square = 7 yd.

The distance from the edge of the square to the center of the square is half of the diagonal. Therefore length of the diagonal = (7 yd * 2) = 14 yd

The diagonal and two sides of the triangle form a right angle triangle. Let the side of the triangle be a. Therefore the hypotenuse is the diagonal, using Pythagoras theorem:

a² + a² = 14²

2a² = 196

a² = 98

a = √98 = 7√2

The length of the side of the triangle = a = 7√2 yd

The area of the rectangle = length × length = 7√2 × 7√2 = 98 yd²

Find the area of the regular polygon. Round to the nearest tenth. 7 yd [? ] yd?-example-1
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