Question

Two prallel side of a trapezium are 58cm and 42cm. the other two side are of equal length which is 17cm. Find the area of trapezium ​

Answer 1

✬ Area = 750 cm² ✬

Step-by-step explanation:

Given:

• Measure of two parallel sides of trapezium are 58 cm and 42 cm.
• Measure of other two side of trapezium is 17 cm.

To Find:

• What is the area of trapezium ?

Solution: Let ABCD be a trapezium where

• AB || CD
• AB = 58 cm , CD = 42 cm
• AD = BC = 17 cm

Let us draw a perpendicular DE and CF from the vertex D and C onto the opposite side AB shown in the figure therefore,

• DC = EF = 42 cm
• { AE & FB are equal }

➟ AB = 58 cm

➟ AB = AE + EF + FB

➟ 58 = 2AE + EF

➟ 58 = 2AE + 42

➟ 58 – 42 = 2AE

➟ 16/2 = AE

➟ 8 cm = AE

Now in right angled triangle AED, by using Pythagoras Theorem

➙ AD² = DE² + AE²

➙ 17² = DE² + 8²

➙ 289 = DE² + 64

➙ 289 – 64 = DE²

➙ 225 = DE²

➙ √225 = DE

➙ 15 cm = DE

Here DE is the height of trapezium ABCD, As we know that

★ Ar. of ABCD = 1/2(Sum of || sides)(Height) ★

$\implies{\rm }$ 1/2(AB + DC)(DE)

$\implies{\rm }$ 1/2(58 + 42)(15)

$\implies{\rm }$ 1/2(100)(15)

$\implies{\rm }$ 100/2(15)

$\implies{\rm }$ 50 $\times$ 15

$\implies{\rm }$ 750 cm²

Hence, area of trapezium is 750 cm².

Answer 2

$\huge\mathfrak\color{red}{Question}$

Two prallel side of a trapezium are 58cm and 42cm. the other two side are of equal length which is 17cm. Find the area of trapezium.

$\huge\mathfrak{\color{orange}{\underline {\underline{Answer♡}}}}$

$\large\mathrm{GiVeN}$

• Parallel sides = 42cm and 58cm

• Non-parallel sides = 17cm

$\large\mathrm{To FiNd}$

• Area of trapezium

$\large\mathrm{CoNsTrUcTiOn}$

Draw AB || DE and DF ⊥ BC.

$\large\mathrm{SoLuTiOn}$

Therefore, AD || BC

and AB||DE (by Cons.)

Therefore ABED is a parallelogram.

AD = 42cm (opp. Sides of ||gm are equal)

EC = 58cm - 42cm = 16cm

EF = FC = 16/ 2 = 8cm

In △CDF

Using Pythagorous Theorm

${dc}^{2} = {df}^{2} + {fc}^{2}$

${17}^{2} = {df}^{2} + {8}^{2}$

$289 - 64 = {df}^{2}$

${15}^{2} = {df}^{2}$

$15 = df$

➨Area of Trapezium = 1/2×Sum of || sides× h

➨Area of Trapezium = 1/2 ×( 42cm+ 58cm)× 15

➨Area of Trapezium = 1/2 × 100 cm × 15

➨Area of Trapezium = 750cm^2

hope it helps you.....✌✌