Question

8. The diagonal of a quadrilateral shaped field is 20 m and the perpendicular dropped on
it from the remaining opposite vertices are 15 m and 5 m. Find the area of the field.


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Answer 1

Answer:

Given :-

• The diagonal of a quadrilateral shaped field is 20 m and the perpendicular dropped on it from the remaining opposite vertices are 15 m and 5 m.

To Find :-

• What is the area of the field.

Formula Used :-

$\clubsuit$ Area Of Quadrilateral :

$\longmapsto \sf\boxed{\bold{\pink{A =\: \dfrac{1}{2}d(h_1 + h_2)}}}$

where,

• A = Area
• d = Diagonal
• h₁ and h₂ = Height

Solution :-

Given :

• Diagonal (d) = 20 m
• Height (h₁) = 15 m
• Height (h₂) = 5 m

According to the question by using the formula we get,

$\implies \sf Area\: of\: field =\: \dfrac{1}{2} \times 20 \times (15 + 5)$

$\implies \sf Area\: of\: field =\: \dfrac{\cancel{20}}{\cancel{2}} \times (20)$

$\implies \sf Area\: of\: field =\: \dfrac{10}{1} \times (20)$

$\implies \sf Area \: of\: field =\: 10 \times 20$

$\implies \sf\bold{\red{Area\: of\: field =\: 200\: {m}^{2}}}$

$\therefore$ The area of field is 200 m².

Answer 2

Answer:

200 m²

Step-by-step explanation:

Area of quadrilateral = 1/2 × Diagonal × (Sum of perpendiculars)

Given, Diagonal = 20m, Perpendiculars = 15m and 5m.

=> Area = 1/2 × 20 × (15+5) = 10 × 20 m² = 200 m²