Question

The area of a trapezium shaped field is 420 sq m. If the distance between two parallel sides is 15 m and one of the parallel sides is 24 m, find the other parallel side.​

Answer 1

✮ Explanation -:

Given :

• Area of a trapezium = 420m²
• Distance between two parallel sides = 15 m
• One of the parallel side of a trapezium = 24m

To Find :

• Other parallel side

Solution :

Let us assume another parallel side as 'b'

$\large\rm\pink{Area \: of \: a \: trapezium = \frac{1}{2}h(a + b) }$

Where,

h = distance between parallel sides

a and b = the length of parallel sides of the trapezium

$\small\pmb{420 = \frac{1}{2} \times 15 \times (24 + b) }$

$⤍ \: \small\rm{420 \times 2 = 15 \times (24 + b)}$

$⤍ \: \small\rm{840 = 15 \times (24 + b)}$

$⤍ \: \small\rm{ \frac{840}{15} = 24 + b}$

$⤍ \: \small\rm{56 = 24 + b}$

$⤍ \: \small\rm{56 - 24 = b}$

$⤍ \: \small\pmb{b = 32}$

Other parallel side of a trapezium = 32m

Check :

$\small\rm{Area \: of \: a \: trapezium = \frac{1}{2} \times 15 \times (24 + 32) }$

$⤍ \small\rm{ \frac{1}{2} \times 15 \times 56 }$

$⤍ \small\rm{15 \times 28}$

$⤍ \: \small\rm{420 {m}^{2} }$

Hence, proved