Find the area of a trapezium whose parallel sides are 34cm, 20cm, and another sides are 13cm and 15cm - Maths - Heron\s Formula

Question

Find the area of a trapezium whose parallel sides are 34cm,
20cm, and another sides are 13cm and 15cm

Lalit Mehra · Accepted Answer

ABCD is a trapezium AB = 34 cm, BC = 15 cm, CD = 20 cm and AD = 13 cm Draw CE || AD and CF âŠ¥ AB In quadrilateral AECD, AE || CD and AD || CE âˆ´ Quadrilateral AECD is a parallelogram AE = CD = 20 cm (Opposite sides of parallelogram are equal) and AD = CE = 13 cm (Opposite sides of parallelogram are equal) BE = AB â€“ AE = 34 cm â€“ 20 cm = 14 cm In Î”BCE, CE = 13 cm, BE = 14 cm and BC = 15 cm $S emi-perimeter, s = \frac{13 cm + 14 cm + 15 cm}{2} = \frac{42 cm}{2} = 21 cm Area of Δ BCE = \sqrt{21 cm (21 cm - 13 cm) (21 cm - 14 cm) (21 cm - 15 cm)} = \sqrt{21 cm × 8 cm × 7 cm × 6 cm} = 84 {cm}^{2}$ Area of Î”BCE = 84 cm2 $∴ \frac{1}{2} \times {BE × CF = 84 cm}^{2} \Rightarrow \frac{1}{2} \times 14 {cm × CF = 84 cm}^{2} \Rightarrow CF = \frac{84 \times 2}{14} cm = 12 cm$ Area of trapezium $= \frac{1}{2} \times (AB + CD) × CF = \frac{1}{2} \times (34 cm + 20 cm) × 12 cm = \frac{1}{2} \times 54 cm × 12 cm = 324 {cm}^{2}$ Thus, the area of trapezium is 324 cm2

Find the area of a trapezium whose parallel sides are 34cm, 20cm, and another sides are 13cm and 15cm.