Question

A Rohombus Shaped Field Has Green Grass For 18 Cows To Graze.If Each Side Of The Rohombus is 30m and it's longer diagonal is 48m.How Much Area of Grass Field Will each Cow be Getting?

$\sf \red{Class:9Th}$
$\sf \pink{Ch: Heron's Formula}$
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Answer 1

Heron's Formula

We've been given that, a rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30m and it's longer diagonal is 48m. With this information, we've asked to calculate, How much area of grass field will each cow be fetting?

Consider ABCD be a rhombus of side 30m and diagonal 48m. i.e.

• AB = BC = CD = AD = 30m
• AC = 48m

Since, diagonal AC divides the rhombus ABCD into two congruent triangles.

In ∆ABC, we have;

• a = 30cm, b = 30cm and c = 48cm.

We know that, the semi perimeter of a triangle is half the sum of all its sides.

$\implies \rm{s = \dfrac{a + b + c}{2}}$

Where, s is semi perimeter, a, b and c are sides of triangle respectively.

By substituting the known values in the formula, we get:

$\implies \rm{s = \dfrac{30 + 30 + 48}{2}}$

$\implies \rm{s = \cancel{\dfrac{108}{2}}}$

$\implies \rm{s = 54m}$

Now, by using Heron's Formula in ∆ABC, we get:

$\implies \rm{Area_{(\triangle ABC)} = \sqrt{s(s - a)(s-b)(s-c)}}$

$\implies \rm{Area_{(\triangle ABC)} = \sqrt{54(54 - 30)(54-30)(54-48)}}$

$\implies \rm{Area_{(\triangle ABC)} = \sqrt{54(24)(24)(6)}}$

$\implies \rm{Area_{(\triangle ABC)} = \sqrt{186624}}$

$\implies \rm{Area_{(\triangle ABC)} = 432m^2}$

As both triangles have same sides. Therefore,

⇒ Area of rhombus = 2(Area of triangle)

⇒ Area of rhombus = 2(432)

⇒ Area of rhombus = 834m²

Given that, number of cows = 18. So, Area of each cow = Area of rhombus.

$\implies \rm{Area_{(Each \: cow)} = \dfrac{Area_{(rhombus)}}{18}}$

$\implies \rm{Area_{(Each \: cow)} = \cancel{\dfrac{834}{18}}}$

$\implies \rm{\boxed{\bf{Area_{(Each \: cow)} = 48 m^2}}}$

Hence, each cow will get 48m² area of the grass field.

$\rule{90mm}{2pt}$

MORE TO KNOW

• A triangle has three sides or edges.

• A triangle has three angles.

• A triangle has three vertices or corners.

• The sum of all internal angles of a triangle is always equal to 180 degrees. This is known as the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• There are three types of triangle, Scalene Triangle, Isosceles Triangle, Equilateral Triangle.

• Area of triangle = 1/2 × b × h. Where, b is breadth and h is the height of triangle.

• Perimeter of triangle = sum of all sides. i.e. P = a + b + c. Where, a, b and c are sides of the triangle respectively.

Answer 2

Step-by-step explanation:

given :

• Rohombus Shaped Field Has Green Grass = 18 cows

• Each Side Of The Rohombus = 30 m

• longer diagonal = 48 m

to find :

• How Much Area of Grass Field Will each Cow be Getting = ?

solution :

• side of Rohombus = 30 + 30 + 48 / 2

• side of Rohombus = 108/2

• side of Rohombus = 54

then, we will using the formula :

• traingle formula = √s(s-a) (s-b) (s-c)

• traingle area = √54(54-30)(54-30)(54-48)

• traingle area = √54 (24) (24) (6)

• traingle area = √186624

• traingle area = 432

• Rohombus = area traingle + area traingle

• rohombus = 432 + 432

• rohombus = 864

then, we have

• cow = Rohombus area / 18

• cow = 864/18

• cow = 48

Area of Grass Field Will each Cow be Getting = 48cm

learn more :

• formula = √s(s-a) (s-b) (s-c)

• traingle area formula = 1/2 × base × height