Question

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

Answer 1

From the point C construct CE || DA

We know that ADCE is a parallelogram having AE || DC and AD || EC with AD = 13m and D = 11m

It can be written as

AE = DC = 11m and EC = AD = 13m

So we get

BE = AB – AE

By substituting the values

BE = 25 – 11 = 14m

Consider △ BCE

We know that BC = 15m, CE = 13m and BE = 14m

Take a = 15m, b = 13m and c = 14m

So we get

We know that

Area of △ BCE = ½ × BE × CL

By substituting the values

84 = ½ × 14 × CL

On further calculation

84 = 7 × CL

By division

CL = 12m

We know that

Area of trapezium ABCD = ½ × sum of parallel sides × height

It can be written as

Area of trapezium ABCD = ½ × (AB + CD) × CL

By substituting the values

Area of trapezium ABCD = ½ × (11 + 25) × 12

On further calculation

Area of trapezium ABCD = 36 × 6

By multiplication

Area of trapezium ABCD = 216 m²

Therefore, the area of trapezium ABCD is 216 m².