Question

a Trapezium has parallel sides 25m and 10m and non parallel sides 14m and 13m .find its area

Answer 1

Solution:-
Let the ABCD be a trapezium with sides AB = 25 m, BC = 13 m, CD = 10 m and DA = 14 m.
We have to draw a parallel line from DE parallel to BC. Side BC = 13 m so, DE will also be 13 m.
So, a new triangle ADE is constructed with sides DA = 14 m, AE = 15 m and DE = 13 m.
According to Heron's formula,
√s(s-a)(s-b)(s-c)
s = (14 + 15 + 13)/2
s = 42/2
s = 21 m
√21(21-14)(21-15)(21-13)
√21 × 7 × 6 × 8
√7056
Area of the triangle ADE = 84 m²
Now, we have to find the height of the triangle ADE.
Area of triangle = 1/2 × base × height
84 = 1/2 × 15 × h
15h = 84 × 2
15h = 168
h = 168/15
h = 11.2 m
Area of the remaining part = 11.2 × 10 
= 112 m²
So, total area = Area of the triangle + area of the parallelogram = 84 + 112
196 m²
Answer.