Question

A piece of land is in the shape of rhombus it is divided into two equal parts if the perimeter of the land is 400m and one of the diagonal is 160m how much area of them will get for their crops
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Answer 1

Answer:-

Your Answer Is 4,800 m².

Explanation:-

Given:-

• A field in shape of Rhombus with 400 m as Perimeter.

• The fireld is divided in two equal parts with length of diagonal = 160 m.

To Find:-

• The area of field the farmet gets for crops i.e. area of one side of the field.

Formulas Used:-

$\\ \large \orange{1. \: \: \boxed{ \purple{ \bf p = 4 \times side.}}}$

Where,

• p = Perimeter of the Rhombus.

$\\ \large \orange{2. \: \: \boxed{ \purple{ \bf A = \sqrt{s(s - a)(s - b)(s - c)}.}}}$

Where,

• A = Area of a triangle.

• s = Semiperimeter i.e perimeter/2.

• a, b and c are vertices of a triangle i.e. sides of a triangle.

So Here,

• p = 400 m.

• Side = ??.

• A = ?? [This id to be find].

• c = 160 m = Diagonal of the Rhombus.

Now,

By using formula 1 we get:-

$\\ \tt\mapsto 4 \times side = 400 \: m.$

$\\ \tt\mapsto side = \frac{400}{4} \: m.$

$\\ \bf\mapsto side = 100 \: m.$

Therefore,

Area of the field farmer get for their crops,

$\\ = \rm area \: \: of \: \: \triangle ABC.$

(See the Attachment for figure)

And Sides of this triangle are:-

• 100m, 100m and 160m respectively.

$\\ \tt\leadsto s = \dfrac{100 + 100 + 180}{2} \: m = \dfrac{360}{2} \: m = 180 \: m.$

And Hence area of the triangle,

$\\ \tt = \sqrt{s(s - a)(s - b)(s - c)}.$

$\\ \tt = \bigg(\sqrt{180(180 - 100)(180 - 100)(180 - 160)} \bigg) \: {m}^{2}.$

$\\ \tt = \sqrt{180 \times 80 \times 80 \times 20} \: \: m {}^{2} .$

$\\ \tt = \sqrt{23040000} \: \: m {}^{2} .$

$\\ \large \red{ \boxed{ \blue{\bf = 4800 \: \: m {}^{2}.}}}$

Therefore the farmer will get 4,800 m² of area for his crops.

Answer 2

Answer:

using Pythagoras theorem=

80²+x=100²

x=100²-80²

x=10000-6400

x=√3600

x=60

diagonal2=60×2

=120

area=1/2×160×120

=9600m²