Question

The diagonal of a quadrilateral shaped field is 18 m and the perpendiculars dropped on it from the remaining opposite vertices are 6 m and 9 m. Find the area of the field.

Answer 1

Given:

• The diagonal of a quadrilateral shaped field is 18 m.

• The perpendiculars dropped on it from the remaining opposite vertices are 6 m and 9 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 , ∆ ABC and ∆ ADC are the two triangles in the quadrilateral. Therefore,

$\bullet \leadsto$ Area of the quadrilateral = Area of ∆ ABC + Area of ∆ ADC.

In ∆ ABC :

➝ Area of ∆ ABC = ½ × b × h

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

➝ Area of ∆ ABC = ( ½ × 18 × 9 ) m²

➝ Area of ∆ ABD = (9 × 9) m²

➝ Area of ∆ ABD = 81 m²

In ∆ ADC :

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

➝ Area of ∆ ADC = ( ½ × 18 × 6 ) m²

➝ Area of ∆ ADC = (9 × 6) m²

➝ Area of ∆ ADC = 54 m²

$\sf {\therefore }$ Area of the quadrilateral = (81 + 54) m²

➝ Area of the quadrilateral = 135 m²

Hence, area of quadrilateral shaped field is 135 m².

Answer 2

✓Verified Answer

Given:

• The diagonal of a quadrilateral shaped field is 18 m.

• The perpendiculars dropped on it from the remaining opposite vertices are 6 m and 9 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 , ∆ ABC and ∆ ADC are the two triangles in the quadrilateral. Therefore,

\bullet \leadsto∙⇝ Area of the quadrilateral = Area of ∆ ABC + Area of ∆ ADC.

In ∆ ABC :

➝ Area of ∆ ABC = ½ × b × h

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

➝ Area of ∆ ABC = ( ½ × 18 × 9 ) m²

➝ Area of ∆ ABD = (9 × 9) m²

➝ Area of ∆ ABD = 81 m²

In ∆ ADC :

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

➝ Area of ∆ ADC = ( ½ × 18 × 6 ) m²

➝ Area of ∆ ADC = (9 × 6) m²

➝ Area of ∆ ADC = 54 m²

\sf {\therefore }∴ Area of the quadrilateral = (81 + 54) m²

➝ Area of the quadrilateral = 135 m²

Hence, area of quadrilateral shaped field is 135 m².