Question

PQRS is a rectangle inscribed in a quarter circle of radius 13 cm as above. PQ is 5 cm. A is a point on PQ. What is the area of triangle PAS

Answer 1

Answer:

Step-by-step explanation:

Given Pqrs is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on pq. If ps = 5 cm, then area (ras) is

qs = 13 cm (in a quadrant of circle radius is given as 13 cm)

From triangle qps

From pythogoras theorem we have,

 qs^2 = ps^2 + pq^2

13^2 =  5^2 + pq^2

169 = 25 + pq^2

pq^2 = 144

pq = 12 cm

sr is also equal to 12 cm (because pq = sr)

Now area of triangle = 1/2 base x height

 area of triangle asr = 1/2 x sr x ps

                         = 1/2 x 12 x 5

                      = 30 cm^2

Area of triangle ras = 30 cm^2.

HOPE IT HELPS YOU.

Answer 2

Answer:-

→ This statement is False because A is a point on PQ, then ar (PAS) ≠ 30 cm²

→ But, exceptionally, the statement can be true if PA is equal to PS.

Explaination:-

★ ATQ,

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm.

★ Note:-

Check out the attachment for the diagram.

★ Given that:-

A is a point on PQ

So, PA < PQ

★ Using formula:-

ar (△PQR) = ½ × PQ × QR

= ½ × 12 × 5

= ½ × 60

= 30cm²

Wkt, PS = 5 cm ( Given )

★ If PA < PQ,

ar(△PAS) < ar(△PQR)

Then, ar(△PAS) < 30 cm²

★ Suppose PA = PQ,

ar (△PAS) = ½ × PQ × PS → [By formula]

= ½ × 12 × 5

= ½ × 60

= 30cm²