Question

In the following figure, the side of square ABCD is 7 cm, with centre D and radius DA. Sector D-AXC is drawn. Fill in the following boxes properly and find out the area of the shaded region:

Solution:

Area of square = (side)²

= (7)²

Area of square = `square` cm²

If the area of the sector (D-AХC) = 38.5 cm2, then

A (shaded region) = `A  square - A  square`

= 49 cm² − 38.5 cm²

= `square` cm²

Answer 1

Area of square = (side)²

= (7)²

Area of square = \[\boxed{49}\] cm²

In the sector formula:

Sector D–AXC: angle at D = 90°, radius = DA = 7

θ = 90, π = `22/7`, r² = 7 × 7,

Area of sector = `(θ/360) xx π r^2`

= `(90/360) xx (22/7) xx (7 xx 7)`

= 38.5 cm²

∴ Area of the sector = 38.5 cm²

If the area of the sector (D-AХC) = 38.5 cm2, then

A (shaded region) = A \[\boxed{square}\] − A \[\boxed{sector}\]

= 49 cm² − 38.5 cm²

= \[\boxed{10.5}\] cm²