Question

two parallel side of isosceles trapezium are 10 cm and 20 cm and its non parallel side is equal to 13 cm find area of the trapezium​

Answer 1

Answer:

Area of trapezium is = 1/2 × ( sum of parallel sides ) × height

Answer 2

The area of the trpezium is 180 cm²

Step-by-step explanation:

Let us draw an isosceles trpezium, where a and b are the parallel sides and c is the non parallel side and h is the height.

Here,

a = 10 cm

b = 20 cm

c = 13 cm

In the attached figure, let us find the value

$\frac{1}{2}(b-a)\\\\=\frac{1}{2}(20-10)\\\\=5$

Apply Pythagoras theorem,

$h=\sqrt{c^2- (\frac{1}{2}(b-a))^2}\\\\h=\sqrt{13^2-5^2}\\\\h=\sqrt{169-25}\\\\h=\sqrt{144}\\\\h=12$

Therefore, the area of the trpezium is given by

$A=\frac{a+b}{2}\times h\\\\A=\frac{10+20}{2}\times12\\\\A=15\times12\\\\A=180\text{ sq. cm}$

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