Question

the area of the trapezold is 48 square meters. what is the trapezoids height, h? h = meters

Explanation:

Step1: Write the formula for the area of a trapezoid

The formula for the area of a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\), where \(b_1\) and \(b_2\) are the lengths of the parallel sides and \(h\) is the height. Here, \(b_1 = 4\) m, \(b_2=12\) m and \(A = 48\) m².

Step2: Substitute the values into the formula

Substitute \(A = 48\), \(b_1 = 4\), \(b_2 = 12\) into \(A=\frac{(b_1 + b_2)h}{2}\), we get \(48=\frac{(4 + 12)h}{2}\).
Simplify the equation: \(48=\frac{16h}{2}\), which further simplifies to \(48 = 8h\).

Step3: Solve for \(h\)

Divide both sides of the equation \(48 = 8h\) by 8. So, \(h=\frac{48}{8}\).

Answer:

\(6\) meters