Answer:
\(\text{The area of trapezoid ABCD is }54 units^2\)
Step-by-step explanation:
Given that ABCD is a trapezoid, AD = 10, BC = 8 and the area of ∆ACD = 30.
we have to find the area of trapezoid ABCD.
\(\text{Area of triangle ACD}=\frac{1}{2}\times base\times height\)
\(30=\frac{1}{2}\times 10\times h\)
\(h=\frac{30\times 2}{10}=6 units\)
The area of trapezoid can be calculated by the formula
\(=\frac{1}{2}\times (\text{sum of parallel sides})\times height\)
\(=\frac{1}{2}\times (AD+BC)\times h\)
\(=\frac{1}{2}\times (10+8)\times 6\)
\(=\frac{1}{2}\times 18\times 6=54 units^2\)
\(\text{Hence, the area of trapezoid ABCD is }54 units^2\)
