SOLUTION: A pentagon is formed by adjoining a square to the base of an isosceles triangle. If the legs of the triangle have length 5 and the pentagon has perimeter 34, what is the area of th

Question 1194934: A pentagon is formed by adjoining a square to the base of an isosceles triangle. If the legs of the triangle have length 5 and the pentagon has perimeter 34, what is the area of the pentagon?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let x be the side length of the square.

Then the perimeter of the pentagon is 3(x)+2(5)=34, which makes the side length of the square 8.

If you cut the isosceles triangle in half, you get two congruent right triangles each with one leg 8/2=4 and hypotenuse 5, making the other leg of each of those triangles 2.

So the area of the isosceles triangle (half base times height) is (1/2)(8)(3)=12.

The area of the square is 8*8=64, so the area of the pentagon is 64+12=76.

ANSWER: 76

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