Let the sides of trapezium be 5k and 3k, respectively

According to the question,
(1/2) x [(5k + 3k) x 12] = 384

Correct Option: B

Let the sides of trapezium be 5k and 3k, respectively

According to the question,
(1/2) x [(5k + 3k) x 12] = 384
⇒ 8k = (384 x 2)/12 = 64
⇒ k = 64/8 = 8 cm

Length of smaller of the parallel sides = 8 x 3 = 24 cm

Circumference of the circle = 2πr = 25
⇒ r = 25 / (2π)

According to the formula,
Side of inscribed square = r√2

Correct Option: A

Circumference of the circle = 2πr = 25
⇒ r = 25 / (2π)

According to the formula,
Side of inscribed square = r√2
= 25 / (2πr x √2)
= 25 / (π√2 ) cm

Area of square = 64 sq cm
(Side)² = 64
∴ Side = √64 = 8 cm


According to the question,
⇒ 2πr = 4 x 8
⇒ r = (4 x 8)/2π

Correct Option: C

Area of square = 64 sq cm
(Side)² = 64
∴ Side = √64 = 8 cm


According to the question,
⇒ 2πr = 4 x 8
⇒ r = (4 x 8)/2π
⇒ r = 16/π

∴ Area of the circle
= π x (16/π) x (16/π) sq cm
= 256/π sq cm.

Diameter of the circle = 13 + 5 = 18 cm
∴ Radius = Diameter/2 =18/2 = 9 cm
Area of the circle = πr² = (22/7) x 9²

Correct Option: D

Diameter of the circle = 13 + 5 = 18 cm
∴ Radius = Diameter/2 =18/2 = 9 cm
Area of the circle = πr² = (22/7) x 9²
= (22 x 81)/9
= 1782/7
= 254.57 sq cm
= 255 sq cm

Ratio of the areas of the circumcircle and incircle of a square
= [(Diagonal)²π] / [(Side)²π]

Correct Option: A

Ratio of the areas of the circumcircle and incircle of a square
= [(Diagonal)²π] / [(Side)²π]
= [(Side x √2)²] / (Side)² = 2/1 or 2 : 1