Question

6. The diagonal of a quadrilateral shaped field is 24 m and the remaining opposite

verticles are 8 m and 13 m. Find the area of the field​

Answer 1

☆ Solution ☆

Given :-

• The diagonal of a quadrilateral shaped field is 24 m and the remaining opposite verticles are 8 m and 13 m.

To Find :-

• The area of the field.

Step-by-Step-Explaination :-

Area of the field = area of ∆ABD + area of ∆BCD

= 1/2 × b × h + 12 × b × h

= 1/2 × 24 × 13 + 12 × 24 × 8

= 12 × 13 + 12 × 8

= 12 × (13 + 8)

= 12 × 21

= 252 m²

Hence,

The area of the field = 252 m²

Answer 2

Given :-

• Diagonal of a quadrilateral shaped field = 24 m
• Remaining opposite verticles = 8 m and 13 m.

To Find :-

• Area of the field.

Solution :-

Area = Area of ∆ABD + Area of ∆BCD

:$\implies$ $\rm \dfrac{1}{2} \: × \: b \: × \: h \: + \: 12 \: × \: b \: × \: h$

:$\implies$ $\rm \dfrac{1}{2} \: × \: 24 \: × \: 13 \: + \: 12 \: × \: 24 \: × \: 8$

:$\implies$ $\rm \ {12\: × \: 13 \: + \: 12 \: × \: 8}$

:$\implies$ $\rm \ {12 \: × \: (13 \: + \: 8)}$

:$\implies$ $\rm \ {12 \: × \: 21}$

:$\implies$ 252 m²

Hence,

The area of the field = 252 m².