Question

Question :-

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?


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Answer 1

❏ Given :

• 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.

❏ To Find :

• How much area of grass field will each
• cow be getting?

❏ Solution :

⇝Let the field be ABCD

⇝It is Given that,

$\sf\pink{➵Side \: of \: Rhombus = 30m }$

$\sf\pink{➵AB = BC = CD = AB = 30m</p><p>}$

$\sf\red{➢Also, Diagonal = 48m}$

$\sf\red{➢BD = 48m}$

⇝Area of rhombus = Area : ABD + Area : BCD

$\sf\orange{ †Let's \: Finding \: the \: area \: ABD}$

Area of triangle triangle

$\sf\pink{ = \sqrt{s(s - a)(s - b)(s - c)} }$

Here, s is the semi-perimeter,

and a,b,c are the sides of a triangle

Here,

$\sf\pink{S = \frac{a + b + c}{2} = \frac{30 + 30 + 48}{2} = \frac{100}{2} = 54m }$

Area of triangle ABD

$\sf\pink{ = \sqrt{s(s - a)(s - b)(s - c)} }$

Putting a = 30m, b = 30m, c = 48m & s = 54

$\sf\pink{ = \sqrt{54(54 - 30)(54 - 30)(54 - 48)} }$

$= \sf\pink{ \sqrt{54(24)(24)(6)} }$

$\sf\pink{ = \sqrt{(6 \times 9) \times (24 \times 24) \times (6)} }$

$\sf\pink{ = \sqrt{(6 \times 6) \times (9) \times (24 \times 24) } }$

$\sf = \pink{ \sqrt{(6²) \times (</p><p>3²) \times (24²)} }$

$\sf = \pink{ \sqrt{(6²)} \times \sqrt{(3²)} \times \sqrt{(24²)m} }$

$\sf\pink{ = 6 \times 3 \times 24}$

$\sf\pink{ = 432 {m}^{2} }$

❏ Hence,

Area of ABD 432m²

Similarly,

Area BCD = 432m²

So, Area of Rhombus ABCD = Area ABD + Area BCD

= 432 + 432

= 864m²

Answer 2

❒ Given :-

• ➵ A rhombus shaped field has green grass for 18 cows to graze.
• ➵ Each side of the rhombus is 30 m and its longer diagonal is 48 m.

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❒ To Find :-

• ➵ How much grass will each cow get ?

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❒ Solution :-

✬ Formula Used :

${\large{\red{\bigstar \: \: {\orange{\underbrace{\underline{\blue{\bf{Area{\small_{(Triangle)}} = \sqrt{s(s - a)(s - b)(s - c)} }}}}}}}}}$

• After the diagonal is applied the rhombus will be divided into 2 equilateral triangles whose sides will be :

✏Sides :

➳ 1st side = 30 m

➳ 2nd side = 30 m

➳ 3rd side = 48 m

✬ Area of the triangle :

✏ First finding the semi - perimeter :

${\large{\longrightarrow{\bf{S = \frac{a + b + c}{2} }}}}$

${\large{\longrightarrow{\bf{S = \frac{30 + 30+48}{2} }}}}$

${\large{\longrightarrow{\bf{S = {\cancel\frac{108}{2} }}}}}$

${\large{\orange{\dashrightarrow{\green{\underline{\bf{S = 54 m}}}}}}}$

✏ Than Area :

${\large{\longrightarrow{\bf{Area = \sqrt{s(s - a)(s - b)(s - c)} }}}}$

${\large{\longrightarrow{\bf{Area = \sqrt{54(54 - 30)(54 - 30)(54 - 48)} }}}}$

${\large{\longrightarrow{\bf{Area = \sqrt{54 \times 24 \times 6} }}}}$

${\large{\longrightarrow{\bf{Area = \sqrt{6 \times 3\times 24} }}}}$

${\large{\orange{\dashrightarrow{\green{\underline{\bf{Area = 432 m²}}}}}}}$

✬Area of Rhombus :

${\large{{\longmapsto{\bf{Area{\small_{(Rhombus)}} = Area{\small_{(Triangle)}} \times 2}}}}}$

${\large{{\longmapsto{\bf{Area{\small_{(Rhombus)}} = {432 \: m}^{2} \times 2}}}}}$

${\large{\red{:{\longmapsto{\purple{\underline{\overline{\boxed{\bf{Area = 864 m²}}}}}}}}}}$

✬ Each cow will graze :

${\large{\longrightarrow{\bf{Area{\small_{(Rhombus)}} \div No.{\small_{(Cows)}}}}}}$

${\large{\longrightarrow{\bf{864 \div 18}}}}$

${\large{\red{:{\longmapsto{\purple{\underline{\overline{\boxed{\bf{Area = 48 \: m²}}}}}}}}}}$

❒ Hence :

➻ Each cow will graze 48 m².

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