Question

find the area of a Trapezium whose parallel sides are 11m and 25 m long and the non parallel sides are 15 M and 13m long

Answer 1

this is the explanation for the question

Answer 2

Given that,

Parallel sides are 11 m and 25 m long and the non parallel sides are 15 m and 13 m long.

We need to draw a diagram

According to diagram

The opposite sides of quadrilateral DEBC are parallel.

It is a parallelogram.

DE=BC=13 m

AE=(AB-EB)

AE=AB-DC

Put the value into the formula

$AE=25-11$

$AE=14$

For ΔDAE,

Let, AE = 14 m

DE = 13 m

DA = 15 m

We need to calculate the area of triangle

Using formula for triangle

$s=\dfrac{a+b+c}{2}$

Put the value into the formula

$s=\dfrac{14+13+15}{2}$

$s=21\ m$  

We need to calculate the area of ΔDAE

Using formula of area

$A=\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{21\times(21-14)\times(21-13)\times(21-15)}$

$A=84\ m^2$

We need to calculate the value of DL

Using formula of area

$A=\dfrac{1}{2}\times AE\times DL$

Put the value into the formula

$84=\dfrac{1}{2}\times14\times DL$

$DL=\dfrac{2\times84}{14}$

$DL=12\ m$

We need to calculate the area of trapezium

Using formula of area

$A=\dfrac{a+b}{2}\times h$

Put the value into the formula

$A=\dfrac{11+25}{2}\times 12$

$A=216\ m^2$

Hence, The area of trapezium is 216 m².