Question

The area A of a trapezoid with parallel bases of lengths \(b_{1}\) and \(b_{2}\) and height \(h\) is \(A=\frac{1}{2} h\left(b_{1}+b_{2}\right)\) Find the area of a trapezoid whose height is 2 meters and whose bases are 6 meters and 10 meters. (GRAPH CANNOT COPY)

Short answer

The area of the trapezoid is 16 square meters.

Step-by-step solution

Understand the formula

We are given the formula for the area of a trapezoid: \(A=\frac{1}{2} h\left(b_{1}+b_{2}\right)\). The meaning of the symbols are as follows: \(A\) is the area, \(h\) is the height of the trapezoid, and \(b_{1}\) and \(b_{2}\) are the lengths of the two bases.

Substitute the given values

We substitute the given values into the formula. The height \(h\) is 2 meters, base \(b_{1}\) is 6 meters, and base \(b_{2}\) is 10 meters. So we can write: \(A=\frac{1}{2} * 2\left(6+10\right)\)

Simplify and solve

Simplify the equation to compute the area. \(A = 1*(16) = 16\)

Write and check the final answer

The area of this trapezoid is 16 square meters. Check and ensure the answer makes sense in the context of the problem.