Determine the length of side 'a' which is the top of the trapezoid.

Question

The area of a trapezoid is calculated to be 61.5 square units. The side length 'a' is 2x - 3 units long and side 'b' is 5x - 1 units long. The height, h, of the trapezoid is 6 units. Determine the length of side 'a' which is the top of the trapezoid.

Answer 1

The formula for the area of a trapezoid is A = 1/2(a + b)*h.

a is the top part of the trapezoid, b is the bottom part of the trapezoid, and h is the height of the trapezoid.

a = 2x - 3 units

b = 5x - 1 units

c = 6 units

A = 61.5 units²

1/2[(2x - 3) + (5x - 1)]*6 = 61.5

3*[(2x - 3) + (5x - 1)] = 61.5

3*(7x - 4) = 61.5

21x - 12 = 61.5

21x = 73.5

x = 3.5

To find a, we need to substitute 3.5 for x. Therefore, we have a = 2(3.5) - 3 = 7 - 3 = 4 units.