Question

the diagonal of a quadrilateral shaped field is 24 metre and the perpendiculars dropped on it from the remaining opposite vertices are 8 metre and 13 metre find the area of the field​

Answer 1

Given :

Diagonal of quadrilateral = 24 m and perpendicular dropped on it (diagonal) from the remaining opposite vertices are 8 m and 13 m.

(As shown in figure)

Find :

Area of the Quadrilateral.

Solution :

We know that

Area of quadrilateral = 1/2 × diagonal × (Sum of perpendicular on the quadrilateral from remaining opposite vertices)

Assume a quadrilateral ABCD such that

BD = diagonal of quadrilateral

AM and CN = perpendiculars on the diagonal

We have

• Diagonal = BD = 24 m
• Perpendicular on the quadrilateral (AM and AN) = 8 m and 13 m

Substitute the known values in above formula. To find the value of area of field (quadrilateral).

→ 1/2 × 24 × (8 + 13)

→ 12 × 21

→ 252 m²

∴ Area of quadrilateral is 252 m².

Answer 2

$\bf{\huge{\underline{\boxed{\sf{\blue{Answer:}}}}}}$

$\bf{\underline{\sf{\pink{Given:}}}}$

• The diagonal of a quadrilateral shaped field is 24 metre.
• The perpendiculars dropped on it from the remaining opposite vertices are 8 metre and 13

$\bf{\underline{\sf{\pink{To\:find\::}}}}$

• The area of the quadrilateral shaped field.

$\bf{\underline{\sf{\pink{Solution:}}}}$

Let's assume the □ ABCD to be the quadrilateral shaped field.

AC = Diagonal of the quadrilateral measuring 24 m

BE and FD are two perpendiculars dropped on it from the remaining opposite vertices.

BE = 8 m

FD = 13 m

The field is divided into two triangles, Δ ABC and Δ ACD

About Δ ABC :-

Base = AC = 24 m

Height = BE = 8 m

About Δ ACD :-

Base = AC = 24 m

Height = FD = 13 m

Now using the data for two triangles we will calculate the area of the triangles and then sum their areas to find the area of the field.

Area of Δ ABC,

We know that area of a triangle is calculated using the formula,

$\bf{\large{\underline{\boxed{\sf{\red{Area\:of\:traingle\:=\:1/2\times\:base\:\times\:height }}}}}}$

Plug in the values,

A (Δ ABC) = $\large\frac{1}{2}$ × AC × BE

A ( Δ ABC ) = $\large\frac{1}{2}$ × 24 × 8

A (Δ ABC) = 12 × 8

A ( Δ ABC) = 96 sq. m

A (Δ ABC) = 96 m²

Similarly we will calculate the area of Δ ACD using the same formula.

A (Δ ACD) = $\large\frac{1}{2}$ × AC × FD

Plug in the values,

A (Δ ABC) = $\large\frac{1}{2}$ × 24 × 13

A (Δ ACD) = 12 × 13

A ( Δ ACD ) = 156 sq. m

A (Δ ACD) = 156 m²

Now we will calculate the area of the quadrilateral shaped field.

Area of field = Area of Δ ABC + Area of Δ ACD

Area of field = 96 + 156

Area of field = 252 sq.m

•°• Area of quadrilateral shaped field is 252 m²