Question

In a trapezium ABCD, AB || DC, AB = 30 cm, BC
= 15 cm, DC = 44 cm and AD = 13 cm. Find the
area of the trapezium.​

Answer 1

Step-by-step explanation:

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EB = 13 cm

BC = 15 cm

CE = 14 cm

Use Heron's formula. For triangles that is. There is no Heron's formula for quadrilaterals.

(13 + 15 + 14)/2 = 21

area(EBC) = √[21(21 - 13)(21 - 15)(21 - 14)]

= √[21(8)(6)(7)]

= √(7056)

= 84

Let EC be the base of that triangle. Find its corresponding height.

(base)(height)/2 = area

14h/2 = 84

h = 12

The height of triangle EBC is 12 cm. That is also the height of the trapezium.

area(ABCD) = (AB + DC)h/2

= (30 + 44)(12)/2

= 444 cm²