Find the area of the quadrilateral PQRS, whose diagonal QS = 19.5 cm and the offsets on it are 5.4 cm and 10.6 cm.

Open in App

Solution

Diagonal QS = 19.5 cm

Offsets = 5.4 cm and 10.6 cm

$∴$ Area of quadrilateral PQRS $= \frac{1}{2}$ (sum of offsets) $\times$ diagonal

$= \frac{1}{2} (5.4 + 10.6) \times 19.5$ sq cm $= \frac{1}{2} \times 16 \times 19.5$ sq cm = 156 sq cm.

Suggest Corrections

Similar questions

Q. In quadrilateral PQRS diagonal PR and QS intersects at O such that

A r e a (Δ P O S)

A r e a (Δ Q O R)

.If the distance between side PQ and SR is 4 cm, PQ=3cm, SR=7 cm. Find ar (PQRS).

Q. Calculate the area of quadrilateral PQRS, whose diagonal

P R = 20 c m

and the lengths of perpendiculars from

Q

and

S

on PR is

12 c m

and

10 c m

respectively.

Find the area of a quadrilateral one of whose diagonals is $40 c m$ and the lengths of the perpendiculars drawn from the opposite vertices on the diagonal are $16 c m$ and $12 c m$ .

Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, R = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.

Q. Construct a cyclic quadrilateral

P Q R S

such that

P Q = Q R = 4.3 c m

and diagonals

P R = 6.2 c m, Q S = 5.8 c m

. Then find

m ∠ P Q R

Join BYJU'S Learning Program

Find the area of the quadrilateral PQRS, whose diagonal QS = 19.5 cm and the offsets on it are 5.4 cm and 10.6 cm.

Diagonal QS = 19.5 cm Offsets = 5.4 cm and 10.6 cm ∴ Area of quadrilateral PQRS =12 (sum of offsets) × diagonal =12(5.4+10.6)×19.5 sq cm =12×16×19.5 sq cm = 156 sq cm.

Diagonal QS = 19.5 cm

Offsets = 5.4 cm and 10.6 cm

$∴$ Area of quadrilateral PQRS $= \frac{1}{2}$ (sum of offsets) $\times$ diagonal

$= \frac{1}{2} (5.4 + 10.6) \times 19.5$ sq cm $= \frac{1}{2} \times 16 \times 19.5$ sq cm = 156 sq cm.