Advertisements
Advertisements
प्रश्न
In fig. 3, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)
उत्तर
Let us join OB.
In ΔOAB:
OB2 = OA2 + AB2 = (20)2 + (20)2 = 2 × (20)2
⇒ OB = 20 √2
Radius of the circle, r = `20 sqrt2` cm
`"Area of qudrant OBPQ"=90^@/360^@xx3.14xx(20sqrt2)^2`
`=90/360xx3.14xx(20sqrt2)^2 cm^2`
`=1/4xx3.14xx800 cm^2`
`=628 cm^2`
Area of square OABC = (Side)2 = (20)2 cm2 = 400 cm2
∴ Area of the shaded region = Area of quadrant OPBQ − Area of square OA
= (628 − 400) cm2
= 228 cm2
APPEARS IN
संबंधित प्रश्न
Find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles. [Use Π = 22/7]
In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the given figure. Find the area of the design (Shaded region). [Use Π = 22/7]
In the given figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. [Use Π = 22/7]
The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (See the given figure). Find the area of shaded region. [Use π = 3.14 and `sqrt3 `= 1.73205]
In the given figure, OACB is a quadrant of circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i) Quadrant OACB
(ii) Shaded region
[Use Π = 22/7]
In the given figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region. [Use Π = 22/7]
Find the area of triangle whose base measures 24 cm and the corresponding height measure 14.5 cm.
Find the areas of the triangle whose sides are 42 cm, 34 cm and 20 cm. Also, find the height corresponding to the longest side.
A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away on time, it has to increase its speed by 250 km/hr from its usual speed. Find the usual speed of the plane.
Find the area of the shaded field shown in figure.
