Question

In a quadrilateral PQRS, PQ = 5 cm, SR = 5 cm and PR = 6 cm, ∠QPR = 90, ∠PRS = 90
Find the area of the quadrilateral PQRS.

Answer 1

Answer:

The area of the quadrilateral PQRS is 105cm².

Step-by-step explanation:

Given:

In a □PQRS,

• PQ = 5cm
• SR = 5cm
• PR = 6cm
• ∠QPR = 90°
• ∠PRS = 90°

To Find:

The area of □PQRS.

Solution:

To find the area of □PQRS = ?

Finding side PR = ?

Using Pythagoras theorem,

=> PR² = RQ² - PQ²

=> PR² = 17² - 8²

=> PR = 15cm

From the figure,

• SR is perpendicular to PR and PQ is perpendicular to PR.

=> Area of □PQRS = Area of ∆PQR + Area of ΔPSR ...(i)

=> Area of ΔPQR = 1/2 × PR × PQ ...(ii)

=> Area of ΔPSR = 1/2 × PR = RS ...(iii)

From the above equations (i), (ii) & (iii),

• Area of □PQRS = Area of ΔPQR + area of ΔPSR
• Area of □PQRS = 1/2 × PR × PQ + 1/2 × PR × RS ...(iv)

Now,

Equation (iv) can be written as:

=> Area of □PQRS = 1/2 × PR × (PQ+RS)

=> Area of □PQRS = 1/2 × 15 × (8+6)

=> Area of □PQRS = 1/2 × 15 × 14

=> Area of □PQRS = 105cm²

Therefore,

The area of the □PQRS is 105cm².