Question

The length of parallel sides of a trapezium are
30m and 48m. The length of each equal non-
parellel sides is 15m. Find the area of trapezium​

Answer 1

✪ANSWER✪

• Area = 468 m²

★EXPLAINATION★

☆GIVEN☆

• An isosceles trapezium with length of parallel sides 30m and 48 m and length of non parallel sides 15 m.

☆TO FIND☆

• Area of trapezium.

☆CALCULATION☆

Figure of a trapezium ABCD with the given values is attached.AE and DF are drawn perpendicular to the parallel sides and they are altitude of the trapezium.

✯ALTITUDE OF TRAPEZIUN✯

It can be proved that

ΔABE ≅ΔDCF(try it)

⇒ BE = FC--------(1)

Also, AEFD ia a rectangle(All angles are 90º),

⇒ AD = EF--------(2)

It is given that

BC = 48, AD = 30

⇒ BE + EF + FC = 48

⇒ BE + AD + BE = 48

[ Using (1) and (2) ]

⇒ 2BE + 30 = 48

⇒ 2BE = 18

⇒ BE = 9 m

And ΔABE is right triangle. Applying Pythagoras Theorem

AB² = AE² + BE²

⇒ AE² = 15² - 9²

⇒ AE² = 144

⇒ AE = 12 m

⇒ h = 12 m

᯽AREA OF TRAPEZIUM᯽

Area of a trapezium is given by

Area = $\frac{1}{2}$ x (sum of length of parallel sides) x (altitude)

⇒ Area = $\frac{1}{2}(30+48)(12)$

⇒ Area = 78 x 6

⇒ Area = 468 m²