Find the area of the regular polygon.
1 answer:
Answer:
98 yd²
Step-by-step 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
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