Question

What is the area of the trapezoid with height 10 units?

Answer 1

If by "long leg lengths" you mean the hypotenuse then the area is 116 sq. units.  If you mean the bases of the triangles then the area is 170 sq. units.

If the length of 12 is the hypotenuse, we first must find the base of the triangles using the Pythagorean theorem:

10² + b² = 12²

100 + b² = 144

b² = 44

b = √44 = 6.6

This means we have two triangles and a rectangle.  The area of the rectangle is 5(10) = 50 sq. units.  The area of each triangle is 1/2(6.6)(10) = 33.  Adding all 3 together we have:

50+33+33 = 116 sq. units.

If the 12 is the base, then we have the rectangle with the area of 5(10) = 50 and two triangles each with an area of 1/2(12)(10) = 60:

50+60+60 = 170 sq. units.