Question

pls solve this step by step ​

Answer 1

Solution :-

From the given figure,

PQRS is a quadrilateral

PR is the diagonal which divides PQRS into two triangles.

In ∆ PQR,

The base = PR = 9 cm

The height or altitude = QT = 6 cm

We know that

Area of a triangle = (1/2)×base×height sq.units

Area of ∆ PQR = (1/2)×PR×QT

=> Area of ∆ PQR = (1/2)×9×6 cm²

=> Area of ∆ PQR = 54/2 cm²

Therefore,

Area of ∆ PQR = 27 cm² -----(1)

and

In ∆ PSR,

The base = PR = 9 cm

The height or altitude = SU = 8 cm

We know that

Area of a triangle = (1/2)×base×height sq.units

Area of ∆ PSR = (1/2)×PR×SU

=> Area of ∆ PSR = (1/2)×9×8 cm²

=> Area of ∆ PSR = 72/2 cm²

Therefore,

Area of ∆ PSR = 36 cm² ------(2)

The area of the quadrilateral PQRS

= Area (∆PQR)+Area(∆PSR)

=> Area of PQRS = 27+36 = 63 cm²

Therefore, Area of PQRS = 63 cm²

Answer :-

Area of the quadrilateral PQRS is

63 cm²

Used formulae:-

→ Area of a triangle = (1/2)×base×height sq.units

Answer 2

Step-by-step explanation:

Solution :-

From the given figure,

PQRS is a quadrilateral

PR is the diagonal which divides PQRS into two triangles.

In ∆ PQR,

The base = PR = 9 cm

The height or altitude = QT = 6 cm

We know that

Area of a triangle = (1/2)×base×height sq.units

Area of ∆ PQR = (1/2)×PR×QT

=> Area of ∆ PQR = (1/2)×9×6 cm²

=> Area of ∆ PQR = 54/2 cm²

Therefore,

Area of ∆ PQR = 27 cm² -----(1)

and

In ∆ PSR,

The base = PR = 9 cm

The height or altitude = SU = 8 cm

We know that

Area of a triangle = (1/2)×base×height sq.units

Area of ∆ PSR = (1/2)×PR×SU

=> Area of ∆ PSR = (1/2)×9×8 cm²

=> Area of ∆ PSR = 72/2 cm²

Therefore,

Area of ∆ PSR = 36 cm² ------(2)

The area of the quadrilateral PQRS

= Area (∆PQR)+Area(∆PSR)

=> Area of PQRS = 27+36 = 63 cm²

Therefore, Area of PQRS = 63 cm²

Answer :-

Area of the quadrilateral PQRS is

63 cm²

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