Question

In the following figure, TRPQ is a square, TRXA is an isosceles trapezoid, and perimeter of TRPQ is 24. If RPX and TAQ are isosceles triangles with vertex angles P and Q, which is the area of the trapezoid?


Answer 64
66
68
72

Answer 1

The perimeter of the square is 24, that means that each side of the square is 6 (6+6+6+6=24). So TQ & RP =6. The triangles, when put together, form a square identical to TRPQ, so the total area would be 72, because each square has an area of 36 (6*6)