Question

Q.Find the area of a plot which is in the shape of a quadrilateral, one of whose diagonals
is 20 m and lengths of the perpendiculars from the opposite corners on it are of lengths
12 m and 18 m respectively.
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.
.
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solve the step by step​

Answer 1

Answer :-

The area of quadrilateral-shaped plot is 300m².

Step-by-step explanation:

Given that,

• The diagonal of the quadrilateral-shaped plot = 20m.
• The lengths of two perpendiculars = 12m and 18m.

FIGURE :-

$\setlength{\unitlength}{1.2 cm}\begin{picture}(0,0)\linethickness{0.4mm}\qbezier(0,0)(0,0)(1,3)\qbezier(4.6,1)(4.6,1)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(4.6,1)(4.6,1)(0,0)\qbezier(4,3)(4,3)(0,0)\qbezier(4.6,1)(4.6,1)(3,2.25)\qbezier(2,1.5)(2,1.5)(1,3)\qbezier(2.2,1.7)(2.2,1.7)(2.05,1.9)\qbezier(2.05,1.9)(2.05,1.9)(1.82,1.74)\put(-0.4,-0.3){\qbezier(3.25,2.4)(3.25,2.4)(3.44,2.2)}\put(-0.2,-0.1){\qbezier(3.4,2.25)(3.44,2.25)(3.25,2.05)}\put(2,1.2){ \sf 20m }\put(1.7,1){ \sf (diagonal) }\put(3.6,1.2){ \sf 18m }\put(3.8,1){ \sf ({h}_{2}) }\put(1.6,2.6){ \sf 12m }\put(1.7,2.4){ \sf ({h}_{1}) }\end{picture}$

• Refer the attachment.

We know,

$\underline{\boxed{\tt{Area \: of \: quadrilateral = \dfrac{1}{2} \times diagonal \times ({h}_{1} + {h}_{2})}}}$

Where,

• $\sf{{h}_{1} \: and \: {h}_{2}}$ are the perpendiculars dropped on diagonal.

Therefore,

$\sf{\longrightarrow \dfrac{1}{2} \times diagonal \times ({h}_{1} + {h}_{2})}$

$\sf{\longrightarrow \dfrac{1}{2} \times 20 \times (12 + 18)}$

$\sf{\longrightarrow \dfrac{1}{2} \times 20 \times 30}$

$\sf{\longrightarrow \dfrac{1}{ \cancel{2}} \times \cancel{20} \times 30}$

$\sf{\longrightarrow 1 \times 10 \times 30}$

$\sf{\longrightarrow 10 \times 30}$

$\sf{\longrightarrow {300m}^{2}}$

∴ The area of quadrilateral-shaped plot is 300m².

Answer 2

A N S W E R :

• The area of quadrilateral-shaped plot is 300m².

Given :

• The diagonal of the quadrilateral-shaped plot = 20m

• The length of two prependiculars = 12m and 18m

To find :

• Find the area of the plot ?

Solution :

As we know that,

Formula Used :

★ Area of quadrilateral = 1/2 × diagonal × (h_1 + h_2)

So,

• Diagonal = 20m

• Height (1) = 12m

• Height (2) = 18m

According to the question,

=> 1/2 × 20m (12m + 18m)

=> 10m (30m)

=> 300m²

Hence,

• The area of quadrilateral-shaped plot is 300m².