Question

The Perimeter of trapezium is 52 cm. Its not
non-parallel sides are 10cm each and the distance
between two parallel sides is 8cm. Find the
area of trapezium.​

Answer 1

Perimeter =52cm

a+b+10+10=52

a+b=32cm

h=8cm

Area =

2

1

(a+b)×h

Area =

2

1

×32×8=128cm

2

Answer 2

Given:

• The perimeter of the trapezium is 52 cm
• The non-parallel sides are 10 cm each.
• The distance between the parallel side (i.e. altitude/height) is 8 cm

To find:

• The area of the trapezium.

The formula to find the area of the trapezium is

$\boxed{\boxed{=\frac{1}{2}\times (sum\ of\ parallel\ sides)\times altitude}}$

Now, the sum of parallel sides is not given,

It can be found with help of the perimeter of the trapezium.

• Perimeter = Sum of two parallel sides and two non-parallel sides

⇒ 52 = (sum of two parallel sides) + 10 + 10

⇒ 52 = (sum of two parallel sides) + 20

⇒ 52 - 20 = sum of two parallel sides

⇒ 32 = sum of two parallel sides

So,

Area of trapezium,

$= \frac{1}{2}\times (32) \times 8$

= 32 × 4

= 128 cm sq.

Hence,

• The area of the trapezium is 128 cm sq.