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=√(BC^2-CM^2)`

now, we can plug values

we get

`BM=√(15^2-9^2)`

`BM=12`

now, we can find area of trapezium

`A=(1)/(2) (AB+CD)*(BM)`

now, we can plug values

and we get

`A=(1)/(2) (9+18)*(12)`

`A=162cm^2`

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