in a trapizium ABCD AB II DC, AB= 30cm, BC= 15 cm, DC= 44cm, and AD= 13 cm Find - Maths -

Question

in a trapizium ABCD AB II DC, AB= 30cm, BC= 15 cm, DC= 44cm, and
AD= 13 cm Find the area of trapezium

Ankush Jain · Accepted Answer

Let ABCD be the trapezium

Let us draw a line segment BE parallel to AD âˆ´ BE = AD = 13 cm, DE = 30 cm and EC = 14 cm To find the area of Î”BEC, Heron's formula is needed to be used which you will study in class IX If three sides of a triangle are known then, $Area of the triangle = \sqrt{s (s - a) (s - b) (s - c)} w h e r e s = \frac{a + b + c}{2}$ And a, b and c are sides of the triangle For Î”BEC $s = \frac{BE + EC + CB}{2} = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21 cm$ $Area (Δ BEC) = \sqrt{21 (21 - 13) (21 - 14) (21 - 15)} = \sqrt{21 (8) (7) (6)} = \sqrt{7056} = 84 {cm}^{2}$ $Area of (Δ BEC) = \frac{1}{2} \times height × base 84 = \frac{1}{2} \times height × 14 \Rightarrow Height = \frac{84 \times 2}{14} = 12 cm$ Area of trapezium ABCD = $\frac{1}{2}$ Ã— Height Ã— (Sum of parallel sides) = $\frac{1}{2}$ Ã— 12 Ã— (30 + 44) = $\frac{1}{2}$ Ã— 12 Ã— 74 = 444 cm2

in a trapizium ABCD AB II DC, AB= 30cm, BC= 15 cm, DC= 44cm, and AD= 13 cm. Find the area of trapezium.