Advertisements
Advertisements
Question
ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the midpoints of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in the following figure. Find the area of shaded portion.
Advertisements
Solution
Here, AP = `1/2` AB = `1/2 xx 80` = 40 cm
Also, AS = `1/2` AD = `1/2 xx 60` = 30 cm
Area of ΔAPS = `1/2` × AP × AS = `1/2` × 40 × 30 = 600 cm2
Area of portion PQRS = Area of rectangle ABCD – 4 × Area of ΔAPS
= 80 × 60 – 4 × 600
= 4800 – 2400
= 2400 cm2
Area of circular rangoli = π × (10)2 ...[∵ Radius of circle = 10 cm]
= `22/7 xx 100`
= 314 cm2
∴ Area of shaded region = 2400 – 314 = 2086 cm2
APPEARS IN
RELATED QUESTIONS
In Fig. 3, APB and AQO are semicircles, and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region [Use `pi=22/7`]
A sector of 56°, cut out from a circle, contains 17.6 cm2. Find the radius of the circle.
The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumference of the circles.
A path of 8 m width runs around the outsider of a circular park whose radius is 17 m. Find the area of the path.
PQRS is a diameter of a circle of radius 6 cm. The lengths PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the given figure. If PS = 12 cm, find the perimeter and area of the shaded region.
The area of a circle is 49 π cm2. Its circumference is:
Construct the circumcircle of the ABC when BC = 6 cm, B = 55° and C = 70°.
Find the area and perimeter of the circles with following: Radius = 10.5cm
A wire when bent in the form of a square encloses an area of 484cm2. If the same wire is bent into the form of a circle, find the area of the circle.
A dinner plate is in the form of circle. A circular region encloses a beautiful design as shown in the following figure. The inner circumference is 352 mm and outer is 396 mm. Find the width of circular design.
