Since we know the area of ΔACD as well as the measurement of the base, we will use these to find the length of the altitude. The formula for the area of a triangle is A=1/2bh. Our area is 30 and our base is 10, so we have:
30=1/2(10)h
30=5h
Divide each side by 5:
30/5=5h/5
6=h
The height of the triangle is also the height of the trapezoid. We can now find the area of the trapezoid. The formula we need is A=1/2(B+b)h. Substituting our numbers in, we have:
A=1/2(10+8)(6)=1/2(18)(6)=54
The area of the trapezoid is 54.
