Question

The diagonal of a quadrilateral shaped field is 22 m and the perpendiculars dropped on it from the remaining opposite vertices are 10 m and 4 m. Find the area of the field. a) 145m² b) 380m² c) 154m² d) 308m²​

Answer 1

Step-by-step explanation:

Area of the field= Area of upper triangle + Area of Lower triangle

$= \frac{1}{2 } \times 4 \times 22 + \frac{1}{2} \times 10 \times 22$

=44+110

= 154m²

ans c)

Answer 2

Answer:

Given :-

• The diagonal of a quadrilateral shaped field is 22 m and the perpendicular dropped on it from the remaining opposite vertices are 10 m and 4 m.

To Find :-

• What is the area of the field.

Formula Used :-

$\clubsuit$ Area Of Quadrilateral Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Quadrilateral)} =\: \dfrac{d}{2}\bigg(h_1 + h_2\bigg)}}}\: \: \: \bigstar$

where,

• d = Diagonal
• h₁ and h₂ = Length of perpendicular

Solution :-

Given :

• Length of diagonal (d) = 22 m
• h₁ = 4 m
• h₂ = 10 m

According to the question by using the formula we get,

$\implies \bf Area_{(Field)} =\: \dfrac{d}{2}\bigg(h_1 + h_2\bigg)$

$\implies \sf Area_{(Field)} =\: \dfrac{\cancel{22}}{\cancel{2}}\bigg(4 + 10\bigg)$

$\implies \sf Area_{(Field)} =\: \dfrac{11}{1}\bigg(14)\bigg)$

$\implies \sf Area_{(Field)} =\: 11(14)$

$\implies \sf Area_{(Field)} =\: 11 \times 14$

$\implies \sf\bold{\red{Area_{(Field)} =\: 154\: m^2}}$

$\therefore$ The area of the field is 154 m² .