Question

The lengths of the bases of the right trapezoid are 9 cm and 18 cm. The length of a longer leg is 15 cm. Find the area of the trapezoid.

Answer 1

Firstly, we will draw figure

now, we will draw a altitude from B to DC that divides trapezium into rectangle and right triangle

because of opposite sides of rectangle ABMD are congruent

so,

DM=AB=9

CM=CD-DM

CM=18-9

CM=9

now, we can find BM by using Pythagoras theorem

$BM=\sqrt{BC^2-CM^2}$

now, we can plug values

we get

$BM=\sqrt{15^2-9^2}$

$BM=12$

now, we can find area of trapezium

$A=\frac{1}{2} (AB+CD)*(BM)$

now, we can plug values

and we get

$A=\frac{1}{2} (9+18)*(12)$

$A=162cm^2$

so, area of of the trapezoid is $162cm^2$..........Answer