In a trapezium ABCD ,AB||DC,AB=30,BC=15,DC=44,AD=13 .Find the area of the trapezium.
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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
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
Nikhilv:
thanks bro.
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