Question

The area of a trapezium is 320 square cm. Its parallel sides are in the ratio 2:3. The height of
the trapezium is 16 cm. Find the length of the parallel sides​

Answer 1

Step-by-step explanation:

Given:-

The area of a trapezium is 320 square cm. Its parallel sides are in the ratio 2:3. The height of

the trapezium is 16 cm.

To find:-

Find the length of the parallel sides ?

Solution:-

The ratio of the Parallel sides of a trapezium = 2:3

Let they be 2x cm and 3x cm

Height of the trapezium = 16 cm

We have

a = 2x cm

b = 3x cm

h = 16 cm

Area of a trapezium = (1/2)h(a+b) sq.units

=>Area of the given trapezium

=>(1/2)×16×(2x+3x) sq.cm

=>(16/2)×(5x) sq.cm

=>8×5x sq.cm

=>40x sq.cm

Area of the given trapezium = 40x sq.cm

According to the given problem

Area of the given trapezium = 320 sq.cm

=>40x = 320

=>x = 320/40

=>x = 8 cm

=>2x = 2×8 = 16 cm

=>3x = 3×8 = 24 cm

a=16 cm

b = 24 cm

Answer:-

The lengths of the Parallel sides of the trapezium are 16 cm and 24 cm

Check:-

a=16 cm

b = 24 cm

h= 16 cm

Area of the trapezium = (1/2)h(a+b) sq.units

=>(1/2)×16×(16+24) sq.cm

=>(16/2)×(40)

=>8×40

=>320 sq.cm

Verified the given relation

Used formula:-

• Area of a trapezium = (1/2)h(a+b) sq.units
• Where, a and b are the two parallel sides and h is the height of the trapezium