Question

Find the height of the trapezium in which parallel sides are 35 cm and
20 cm and non parallel sides are 24 cm and 23 cm.
​

Answer 1

Answer:

area of trapezium=1\2×sum of parallel side×height

Answer 2

Height of ABDE=22.2 cm

Step-by-step explanation:

BD is parallel to AE

AE=20 cm

BD=35 cm

ABCE is a parallelogram

AB=CE=23cm

BC=AE=20cm

In triangle CDE

CD=15 cm,DE=24 cm

Half perimeter of triangle,s =$\frac{23+24+15}{2}=31cm$

Area of triangle by Heron's formula

$\sqrt{s(s-a)(s-b)(s-c)}$

By using the formula

Area of triangle CED=$\sqrt{31(31-23)(31-24)(31-15)}$

Area of triangle CED=166.66 square cm

Again , area of triangle =$\frac{1}{2}\times base\times height$

Substitute the values then we get

$166.66=\frac{1}{2}\times 15\times h$

$h=\frac{166.66\times 2}{15}=22.2 cm$

Height of triangle=Height of ABDE=22.2 cm

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