Question

The area for a trapezoid is given by the formula below, where a and b are the lengths of the two bases and h is the height of the trapezoid.
A = h ( a + b ) / 2

If the area of a trapezoid with base b measuring 8 feet is 16.5 square feet and base a measuring the same length as the height, then what is the height of the trapezoid?
A.
7 feet
B.
4 feet
C.
3 feet
D.
9 feet

Answer 1

Answer:

C

Step-by-step explanation:

Given

A = $\frac{h(a + b)}{2}$

Substitute the given values with h = a, then

16.5 = $\frac{a(a+8)}{2}$ ( multiply both sides by 2 )

33 = a(a + 8) ← distribute

33 = a² + 8a ( subtract 33 from both sides )

0 = a² + 8a - 33 ← in standard form

0 = (a + 11)(a - 3) ← in factored form

Equate each factor to zero and solve for a

a + 11 = 0 ⇒ a = - 11

a - 3 = 0 ⇒ a = 3

However, a > 0 thus a = 3

Hence the height is 3 feet