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

Open in App

Solution

Steps of construction:
Step 1: Draw $PQ = 5.4 cm$ .
Step 2: With P as the centre and radius equal to $4 cm$ , draw an arc.
Step 3: With Q as the centre and radius equal to $4.6 cm$ , draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to $3.5 cm,$ draw an arc.
Step 6: With R as the centre and radius equal to $4.3 cm$ , draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.

Thus, PQRS is the required quadrilateral.

Suggest Corrections

Similar questions

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

In Fig. PQRS is a quadrilateral in which diagonals PR and QS intersect in O. [4 MARKS]

Show that:
(i) PQ + QR + RS + SP $>$ PR + QS
(ii) PQ + QR + RS + SP $<$ 2 (PR + QS)

Q. Construct a quadrilateral

P Q R S

such that

P Q = 3.5 c m, Q R = 4.5 c m, R S = 4 c m, ∠ Q = 110^{o}

and

∠ R = 80^{o}

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, radius of the circle circumscribing the quadrilateral

P Q R S

is:

Join BYJU'S Learning Program