Math, asked by purvidoshi09, 11 months ago

in a Trapezium ABCD AB//CD. if AB=30 cm, BC=17 cm, CD=20 cm and BC=9 CM then find its area ​

Answers

Answered by Anonymous
31

Answer:

Translate D by vector AB, and let its image be E. Quadrilateral ABED is a parallelogram, so EB is equal in length to DA. Now consider triangle EBC. All three sides are known.

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

Answered by vy91917gmailcom
1

Step-by-step explanation:

area of abcd are 444 cm2

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