Question

2. The area of a trapezium is 850 sq. cm. One of the parallel sides is 64 cm and the perpendicular
distance between the parallel sides is 17 cm. Find the length of other parallel side. ​

Answer 1

Given :

• Area of trapezium = 850 sq.m
• Length of one of the parallel sides = 64 cm
• Perpendicular distance between the parallel sides = 17 cm

To Find :

• The length of the other parallel side

Solution :

Area of a trapezium is given by ,

$\\ \star \: {\boxed{\purple{\sf{Area_{(trapezium)} = \frac{1}{2} \times (a + b) \times d}}}}$

Here ,

• a and b are length of parallel sides
• h is distance between the parallel sides

We have ,

• a = 64 cm
• A = 850 sq.m
• d = 17 cm

Substituting the values ;

$\\ : \implies \sf \: 850 = \frac{1}{2} \times (64 + b) \times 17$

$\\ : \implies \sf \: 850 \times 2 = (64 +b) \times 17$

$\\ : \implies \sf \: 1700 = (64 + b) \times 17$

$\\ : \implies \sf \: \frac{1700}{17} = 64 + b$

$\\ : \implies \sf \: 64 + b = 100$

$\\ : \implies \sf \: b = 100 - 64$

$\\ : \implies {\underline{\boxed{\pink{\mathfrak{b = 36 \: cm}}}}} \: \bigstar$

Hence ,

• The length of the other parallel side is 36 cm

Answer 2

Given:-

Area of a trapezium =$\sf850 cm^2$

One of the parallel sides is 64 cm

Solution:-

Area of trapezium=$\sf\dfrac{1}{2}$×sum of parallel side ×perpendicular

let the value of other parallel side be x cm.

$\implies\sf 850=\dfrac{1}{2}×(64+x)×17$

$\implies\sf 850×2=(64+x)×17$

$\implies\sf 1700=1088+17x$

$\implies\sf 17x=1700-1088$

$\implies\sf 17x=612$

$\implies\sf x=\dfrac{612}{17}$

$\implies\sf x=36$

Hence, the length of the parallel side is 36 cm.