Question

if the length of a diagonal of a quadrilateral is 14 cm and the perpendicular from the opposite vertices on the diagonal are 6cm and 8cm long then the area of the quadrilateral is

​

Answer 1

Answer:

Area=

2

1

×one diagonal×Sum of the lengths of the perpendiculars drawn from it on the remaining two vertices.

=

2

1

×25×(16.4+11.6)

=

2

25

×28=25×14=350sq.cm

Answer 2

Given :-

• Length of a diagonal of a quadrilateral is 14 cm and the perpendicular from the opposite vertices on the diagonal are 6cm and 8cm long

To find :-

• Area of quadrilateral ABCD

Solution :-

We can find the area of any general quadrilateral by splitting it into two triangles

• Length of diagonal = 14cm

• Altitude of ∆ACB (h1) = 6cm

• Altitude of ∆CDB (h2) = 8cm

In ∆ ACB

→ ½ × base × height

Take diagonal as base of triangle

→ ½ × 14 × 6

→ 7 × 6

→ 42 cm²

In ∆ CDB

→ ½ × base × height

Take diagonal as a base of triangle

→ ½ × 14 × 8

→ 7 × 8

→ 56 cm²

Area of quadrilateral ABCD

→ Area of ∆ACB + Area of ∆CDB

→ 42 + 56

→ 98 cm²

So, area of quadrilateral ABCD is 98cm²

Another method :-

**Area of quadrilateral = ½ (diagonal × sum of altitude drawn on the diagonal from the other two vertices)

→ Area of quadrilateral ABCD

As per formula of quadrilateral

→ ½ × (h1 + h2) × d

→ ½ × (6 + 8) × 14

→ ½ × 14 × 14

→ 7 × 14

→ 98 cm²

Hence,

• Area of quadrilateral ABCD = 98cm²