Question

The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal,
each being 13 cm. Find the area of the trapezium.​

Answer 1

Answer:

We divide the trapezium into 3 parts: 2 triangles and a rectangle.

Base of triangle =

2

20−10

=5

Height of the triangle and rectangle (h)

2

=13

2

−5

2

⇒(h)

2

=144

⇒h=12

Area of trapezium =

2

1

×(sum of parallel sides) × (height)

=

2

1

×(10+20)×(12)

=180 sq.cm

Answer 2

Answer:

first divide the trapezium into 2 triangles and you will get a rectangle with a triangle on its 2 opposite sides each.

Step-by-step explanation:

the sides of the rectangle: l=10cm ,b=h

in Δ ADE, DE =√13²-5² = √169-25 = √144

= 12cm = h

ar ΔADE =ar ΔBCF = 1/2*b*h = 1/2*5*12

= 30cm²

ar of rectangle EFCD=l*b=10*12

=120cm²

area of trapezium=are of rectangle + 2*area of triangle=120+ 2*30 =120+60

=180cm²

OR

you can also use the formula directly: (a+b/2)h      (where, a and b are the parallel side and h is height)

hope this helps:)