To find the area of the trapezoid we need to find the height of the trapezoid.
Trapezoid
A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
Area of Trapezoid
The area of a trapezoid is given as half of the product of the height(altitude) of the trapezoid and the sum of the length of the parallel sides.
\rm{ Area\ of\ trapezoid = \dfrac{1} {2}\times height \times (Sum\ of the\ parallel\ Sides)
The area of the trapezoid is 54 units².
Given to us :
ABCD is a trapezoid
AD=10, BC = 8,
CK is the altitude altitude
Area of ∆ACD = 30
Area of ∆ACD,
In ∆ACD,
\begin{gathered}\rm { Area\ \triangle ACD = \dfrac{1}{2}\times base\times height\\\\\ \end{gathered}
Substituting the values,
30 = 1/2 * AD × CK
30 = 1/2 * 10 × CK
(30 * 2)/10 = CK
CK = 6 units
Area of Trapezoid ABCD
\rm{ Area\ of\ trapezoid = \dfrac{1} {2}\times height \times (Sum\ of\ the\ parallell Sides)
Area ABCD = [tex] \frac{1}{2} \times ck \times (ad + bc)[/tex]
Area ABCD = [tex] \frac{1}{2} \times 6 \times (10 + 8)[/tex]
Area ABCD = [tex] \frac{1}{2} \times 6 \times (18)[/tex]
Area ABCD = 54 units²
Hence, the area of the trapezoid is 54 units².
