Question

The diagonal of a quadrilateral shaped field is 24 m
and the perpendiculars dropped on it from the
remaining opposite vertices are 8 m and 13 m. Find
the area of the field.​

Answer 1

SOLUTION:

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QUESTION:

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

GIVEN:

Diagonal = 24m

$\sf Perpendicular \: dropped = h_1 = 8m , h_2 = 13m$

TO FIND:

Find the area of the field.

FORMULA TO FIND:

$\sf Area \: of \: Quadrilateral = \frac{d}{2} (h_1 + h_2)$

SOLVING BY APPLYING THE FORMULA:

$\rightarrow \sf \frac{24}{2} (13 + 8)$

$\rightarrow \sf \frac{24}{2} (21)$

$\rightarrow \sf 12 \times 21$

$\rightarrow \sf 252$

Hence,Area of the quadrilateral=252m².

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Answer 2

Required Answer :

Given:

• The diagonal of a quadrilateral shaped field is 24 m.

• The perpendiculars dropped on it from the

remaining opposite vertices are 8 m and 13 m.

To calculate:

• Area of the field.

Calculation:

So, let us assume the vertices of the quadrilateral shaped field as A, B, C and D.

We can clearly see that , ∆ ABD and ∆ CBD are the two triangles in the quadrilateral. Therefore,

$\bullet \leadsto$ Area of the quadrilateral = Area of ∆ ABD + Area of ∆ CBD.

In ∆ ABD :

➝ Area of ∆ ABD = ½ × b × h

Here, base is the diagonal of the quadrilateral and height is the perpendicular.

➝ Area of ∆ ABD = ( ½ × 24 × 8 ) m²

➝ Area of ∆ ABD = (12 × 8) m²

➝ Area of ∆ ABD = 96 m²

In ∆ CBD :

Here, same as the first one ,base is the diagonal of the quadrilateral and height is the perpendicular.

➝ Area of ∆ CBD = ( ½ × 24 × 13 ) m²

➝ Area of ∆ CBD = (12 × 13) m²

➝ Area of ∆ CBD = 156 m²

$\therefore$ Area of the quadrilateral = (96 + 156) m²

➝ Area of the quadrilateral = 252 m²

Hence, area of quadrilateral squared field is 252 m².

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