Question

A piece of land is in the shape of trapezium whose parallel side are 50m, and 35m. The non-parallel

sides are 30m and 35m. Prove that area of the land is

1700√5/3m2


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Answer 1

Step-by-step explanation:

it might help you. ...........

Answer 2

Yes, we proved that the area of the land is $\frac{1700\sqrt{5} }{3} m^{2}$.

Given,

A piece of land is shaped like a trapezium with parallel sides of 50m and 35m. The non-parallel sides are 30m and 35m.

To Find,

Proving,

Solution,

Firstly we construct the figure of the trapezium using the given details,

Draw BF║AD & AB║DF

So, figure ABFD is parallelogram

∵ BF = 30 , DF = 35

Now, we will find the area of ΔBFC

using heron's formula

s = $\frac{a+b+c}{2}$

On putting the value, we get,

= $\frac{30+15+35}{2}$

= 40 m

area of ΔBFC = $\sqrt{s(s-a)(s-b)(s-c)}$

On putting the value in the above formula,

= $\sqrt{40(40-30)(40-15)(40-35)}$

= $\sqrt{40*10*25*5}$

= 100$\sqrt{5}$ m²

Now, we have to find the height.

Area of ΔBFC = $\frac{1}{2}$ ×b×h

⇒100$\sqrt{5}$= $\frac{1}{2}$ ×15×h

h = $\frac{40\sqrt{5} }{3}$

Area of trapezium = $\frac{1}{2}$×sum of║sides×h

= $\frac{1}{2}$×85× $\frac{40\sqrt{5} }{3}$

= $\frac{1700\sqrt{5} }{3} m^{2}$. hence proved.

Yes, we proved that the area of the land is $\frac{1700\sqrt{5} }{3} m^{2}$.

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