The area of a trapezium is 180 cm2 and its height is 9 cm. If one of t

1.	The area of a trapezium is 180 cm2 and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, find the two parallel sides.
Answer» Given Let length of first parallel side X Length of other parallel side is X + 6 Area of trapezium= 180 cm² Let Height (h) = 9 cm We know that area of trapezium is \(\frac{1}{2}\)× (sum of parallel sides) × height Therefore Area of trapezium is \(\frac{1}{2}\)× (X + 6 +X) × 9 = 180 cm². \(\therefore\) \(\frac{1}{2}\)× (X + 6 +X) × 9 =180 ⇒ \(\frac{1}{2}\)× (2X + 6) × 9 =180 ⇒ 2X + 6 = \(\frac{180}{9}\times2\) ⇒ 2X + 6 = 40 ⇒ 2X = 40 – 6 = 34 ⇒ X = 17 ∴ Length of the parallel sides is X = 17 cm and X + 6 = 17 + 6 = 23 cm. Therefore lengths of the parallel sides are 17 cm, 23 cm.

The area of a trapezium is 180 cm2 and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, find the two parallel sides.

Answer»

Given

Let length of first parallel side X

Length of other parallel side is X + 6

Area of trapezium= 180 cm²

Let Height (h) = 9 cm

We know that area of trapezium is \(\frac{1}{2}\)× (sum of parallel sides) × height

Therefore Area of trapezium is \(\frac{1}{2}\)× (X + 6 +X) × 9 = 180 cm².

\(\therefore\) \(\frac{1}{2}\)× (X + 6 +X) × 9 =180

⇒ \(\frac{1}{2}\)× (2X + 6) × 9 =180

⇒ 2X + 6 = \(\frac{180}{9}\times2\)

⇒ 2X + 6 = 40

⇒ 2X = 40 – 6 = 34

⇒ X = 17

∴ Length of the parallel sides is X = 17 cm and X + 6 = 17 + 6 = 23 cm.

Therefore lengths of the parallel sides are 17 cm, 23 cm.