Question

Parallel sides of a trapezium are 20cm and 10cm. it's non parallel sides are equal each being 13cm. find area of trapezium .

Answer 1

A line ll to one non ll side is drawn.
Now an isosceles triangle is formed of side 13cm,13cm,10cm Then find height.
h=12cm. Then area of trapezium= 1/2sum of ll sides ×height
area=1/2×20+10×12
area=1/2×32×12
area=192cm^2

Answer 2

$\huge{\underline{\underline{\sf{SOLUTION:-}}}}$

$\sf{\underline{\blue{Answer-}}}$

• Area of trapezium is 180cm².

$\sf{\underline{\blue{Given-}}}$

• Parallel sides of a trapezium are 20cm and 10cm. it's non parallel sides are equal each being 13cm.

$\sf{\underline{\blue{Explanation-}}}$

➨⠀$\sf{{AD}^{2} = {AE}^{2} + {DE}^{2}}$

➨⠀$\sf{( {13})^{2} = ({5})^{2} + ({DE})^{2}}$

➨⠀$\sf{169 = 25 + {DE}^{2}}$

➨⠀$\sf{169 - 25 = {DE}^{2}}$

➨⠀$\sf{144 = {DE}^{2}}$

➨⠀$\sf{DE = \sqrt{144}}$

➨⠀$\sf{DE = 12cm}$

➨⠀$\sf{Area\:of\:trapezium = \frac{1}{2} (a + b) \times h}$

➨⠀$\sf{ \frac{1} {2} (10 + 20) \times 12}$

➨⠀$\sf{ \frac{1} {2} \times 30\times 12}$

➨⠀$\sf{30 \times 6}$

➨⠀$\sf{180cm}^{2}$

• Hence, the area of trapezium is 180cm².

${\sf{\underline{\underline{Additional\: Information-}}}}$

• Trapezium is also known as Trapezoid.

• There are 3 types of Trapezium.

⠀⠀⠀⠀Isosceles trapezium.

⠀⠀⠀⠀Scalene Trapezium.

⠀⠀⠀⠀Right Trapezium.

• Trapezium only have one pair of opposite sides often called parallel sides.

• In the formula of trapezium 1 and 2 are bases while H is the height of Trapezium.

• Perimeter of trapezium P = a + b + c + d where, a, b, c and d are the sides of the trapezium.