Answer: 54 cm²
Step-by-step explanation: In this problem, we're asked to find the area of the trapezoid shown. A trapezoid is a quadrilateral with one pair of parallel sides.
The formula for the area of a trapezoid is shown below.
[tex]Area =\frac{1}{2} (^{b} 1 + ^{b}2)h[/tex]
The b's represent the bases which are the parallel sides and h is the height.
So in the trapezoid shown, the bases are 6 cm and 12 cm and the height is 6 cm. Plugging this information into the formula, we have [tex]\frac{1}{2} (6 cm +12cm)(6 cm)[/tex].
Next, the order of operations tell us that we must simplify inside the parentheses first. 6 cm + 12 cm is 18 cm and we have [tex]\frac{1}{2}(18 cm)(6 cm)[/tex].
[tex]\frac{1}{2} (18 cm)[/tex] is 9 cm and we have 9 cm · 6 cm of 54 cm²
So the area of the trapezoid shown is 54 cm².
