What will be the area of quadrilateral ABCD If AB is equal to 3 cm BC equal to 4 cm CD is equal to 4 cm equal to 5 cm and AC equal to 5 cm?

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A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?

For ΔABCa = 30 mb = 48 mc = 30 m

 Area of 

Area of the rhombus
= 2 Area of ΔABC = 2 x 432 = 864 m2
∴ Area of grass for 18 cows = 864 m2. ∴ Area of grass for 1 cow

Aliter : Draw BE ⊥ AC. Then E is the midpoint of AC.

In right triangle AEB.
AB2 = AE2 + BE2
I By Pythagoras Theorem ⇒    (30)2 = (24)2 + BE2
⇒    900 = 576 + BE2
⇒    BE2 = 900 – 576
⇒    BE2 = 324

BD = 2 BE = 2 x 18 = 36 m Area of rhombus ABCD

Area of right 

∴ Area of rhombus ABCD = 4 Area of ΔAEB = 4 x 216 = 864 m2
∴ Area of grass for 18 cows = 864 m2                   Area of grass for 1 cow  = 

Find the area of a quadrilateral ABCD in which AB = 3cm, BC = 4cm, CD = 4cm, DA = 5cm and AC = 5cm

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