Question

37. Find the area of a trapezium whose parallel sides are 11 m and 25 m
long, and the nonparallel sides are 15 m and 13 m long.
[HOTS]​

Answer 1

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=25-11AE=25−11

AE=14AE=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}s=

2

a+b+c

Put the value into the formula

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

2

14+13+15

s=21\ ms=21 m

We need to calculate the area of ΔDAE

Using formula of area

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

s(s−a)(s−b)(s−c)

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

21×(21−14)×(21−13)×(21−15)

A=84\ m^2A=84 m

2

We need to calculate the value of DL

Using formula of area

A=\dfrac{1}{2}\times AE\times DLA=

2

1

×AE×DL

Put the value into the formula

84=\dfrac{1}{2}\times14\times DL84=

2

1

×14×DL

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

14

2×84

DL=12\ mDL=12 m

We need to calculate the area of trapezium

Using formula of area

A=\dfrac{a+b}{2}\times hA=

2

a+b

×h

Put the value into the formula

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

2

11+25

×12

A=216\ m^2A=216 m

2

Hence, The area of trapezium is 216 m².