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
Answers
Answer:
✬ 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: A=850 cm²
Step-by-step explanation:
Given : i) base (a) = 58 cm
ii) base (b) = 42 cm
iii) height (h) = 17 cm
To find : Area of the Trapezium
Solution : A=a+b /2 x h
A=58+42/ 2 x 17
A=850 cm²
Hope it helps you !!!