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A piece of wire that has been bent in the form of a semicircle including the bounding diameter is straightened and then bent in the form the of a square. The diameter of the semicircle is 14 cm. Which has a larger area, the semicircle or the square? Also, find the difference between them.
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Area of semicircle
Perimeter of semicircle
Perimeter of square
Area of square
Difference
In the figure, ABC is a triangle right angled at A. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.
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Area of sq unit
Area of semicircle
sq units
Area of semicircle
sq units
Area of semicircle
sq units
Area of shaded region sq units
In the figure, AB and CD, the two diameters of a circle with centre O are perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of shaded region.
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Area of big circle
Area of small circle
Area of shaded region
In the figure, AB and PQ are perpendicular diameters of the circle whose centre is O and radius OA = 7 cm. Find the area of shaded region. \(\left(use\ \pi=\dfrac{22}{7}\right) \)
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Radius of bigger circle
Radius of smaller circle
Area of bigger circle
Area of semicircle
Area of semicircle
Area of smaller circle
Area of unshaded triangle
Area of shaded portion
In the figure, O is the centre of a semicircular arc and AOB is a straight line. Find the area of the shaded region.
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Radius
Arc length
Perimeter of shaded region
Area of shaded region
A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs 0.35 per \(cm^2 \).
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Area of circle
Area of triangle
Area of shaded region
Rate
In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the :
(i) quadrant OACB
(ii) shaded region
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(i) Area of quadrant
(ii) Area of shaded region
PQRS is a rectangle in which length is two times the breadth and L is mid point of PQ. With P and Q as centres, draw two quadrants as shown in figure. Find the ratio of the area of rectangle PQRS to the area of shaded portion.
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Area of rectangle
Area of quadrant
Area of both quadrant
Area of shaded region
In the figure, find the area of the shaded region where a circular arc of radius 6 cm is drawn with a vertex O of an equilateral triangle OAB of side 12 cm as centre.
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Area of required figure
= area of circle + area of triangle – area of sector
In the figure, the shape of the top of a table in a restaurant is that of a sector of a circle with centre O and angle BOD = 90Â°. If OB = OD = 60 cm, find the perimeter of the table top. \(\left(use\ \pi=\dfrac{22}{7}\right) \)
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Perimeter
In the figure, a circle of radius 7 cm is inscribed in a square. Find the area of the shaded region.
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Area of shaded triangle
Side of the square
Area of rest shaded part
Total area
A race track is in the form of a ring whose inner circumference is 352 m and outer circumference is 396 m. Find the width of the \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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width of track
In the figure, find the perimeter of shaded region where ADC, AEB and BFC are semicircles on diameters AC, AB and BC respectively.
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Perimeter of shaded region
Find the area of the segment of a circle of radius 14 cm, if the length of the corresponding arc APB is 22 cm. \( use\ \pi=\dfrac{22}{7}\)
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Perimeter of circle
Area of segment
A square OABC is inscribed in a quadrant OPBQ of a circle as shown in figure. If OA = 14 cm, find the area of the shaded region. \(\left[use\ \pi=\dfrac{22}{7}\right] \)
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Area of
Area of quadrant
Area of shaded region
The area of an equilateral triangle is \(49\sqrt3\ cm^2 \). Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles. [Take latex]\sqrt3=1.73 [/latex] ]
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Area of triangle
Area of 3 circles
Area of remaining part
In the figure, ABCD is a square of side 14 cm and APD and BPC are semicircles. Find the area of shaded region \( \left[\pi=\dfrac{22}{7}\right]\)
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Area of square
Area of two semicircles
Area of shaded region
Find the difference between the area of a regular hexagonal plot each of whose side is 72 m and the area of the circular swimming tank inscribed in it. \(\left(Take\ \pi=\dfrac{22}{7}\right) \)
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Area of equilateral
Area of hexagonal plot
Area of inscribed circular swimming
Required difference
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find
(i) The area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area if the rope were 10 m long instead of 5 m. (Use \(\pi=3.14 \))
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Area of quadrant
Area of new quadrant
Increase in grazing area
The given figure depicts a racing track whose left and right ends are semicircular. The distance between the two inner parallel line segment is 60 m and they are each 106 m long. If the track is 10 m wide, find :
(i) The distance around the track along its inneredge
(ii) the area of the track
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Distance around the track along its inner edge
Area of the track
Find the area of the shaded design in the fig. given, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the squares as diameter. (Use \(\pi=3.14 \))
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Area of semicircle AD
Area of semicircle CD
Area of shaded region
In the figure, there are three semicircles, A, B and C having diameters 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate :
(i) the area of the shaded region.
(ii) the cost of painting the shaded region at the rate of 25 paise per \( cm^2\), to the nearest rupee.
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Area of shaded region
Cost
In an equilateral triangle of side 24 cm, a circle is inscribed touching its side. Find the area of the remaining portion of the triangle. (Take \(\sqrt3=1.732 \) )
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Area of in circle
Area of triangle ABC
Area of remaining portion
Find the area of the shaded portion shown in the figure. The four corners are quadrants and at the centre there is a circle. \(\left[\pi=\dfrac{22}{7}\right] \)
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Area of shaded portion
Three horses are tethered with 7 m long ropes at the three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses. Also, find the area of the plot which remains ungrazed.
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Semiperimeter
Area
Area of semicircle with radius
Area of ungrazed land
In the figure, find the area of the shaded region. (Use \(\pi=3.14 \))
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Area of 4 semicircles
length of side of smaller square
Area of smaller square
Area of unshaded region
In the figure, AC = BD = 7 cm and AB = CD = 1.75 cm. Semicircles are drawn as shown in the figure. Find the area of the shaded region. \(\left(Take\ \pi=\dfrac{22}{7}\right) \)
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Area of shaded region
In the figure, \(ABC \) is a rightangled triangle, \(D = 90^o, AB = 28\ cm\) and \(BC = 21\ cm\). With \(AC \) as diameter, a semi â€“ circle is drawn and with \(BC \) as radius a quarter circle is drawn. Find the area of the shaded region.
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Area of shaded region
In the figure, OPQR is a rhombus, three of whose vertices lie on the circle with centre O. If the area of the rhombus is \(32\sqrt3\ cm^2 \), find the radius of the circle.
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In the figure, OPQR is a rhombus whose three vertices, P, Q, R lie on a circle of radius 8 cm. Find the area of the shaded region.
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Area of rhombus
In the figure, AC = 24 cm, BC = 10 cm and O is the centre of the circle. Find the area of the shaded region. (Use \(\pi=3.14 \) )
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Area of semicircle
Area of
Area of shaded part
In the figure, find the area of the shaded design, where ABCD is a square of side 10 cm and semi circles are drawn with each side of the square as diameter. (Use \(\pi=3.14 \) )
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Area of semicircle AD
Area of 4 semicircles
Area of square ABCD
Area of shaded region
In the figure, two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and flower beds.
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Area of sector OAB
Area of OAB
Area of flower bed
Total area
With the vertices A, B and C of a triangle ABC as centres, arcs are drawn with radii 5 cm each as shown in the figure. If AB = 14 cm, BC = 48 cm and CA = 50 cm, then find the area of the shaded region (Use \(\pi=3.14 \) )
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Area of sectors
Area
Area
In the figure, ABC is a quadrant of a circle of radius 14 cm and a semi circle is drawn with BC as diameter. Find the area of shaded region.
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Area of semicircle of diameter
Area of quadrant
Area of
Area of shaded region
The area of an equilateral triangle ABC is \(17320.5\ cm^2\). 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. Find the area of the shaded region. (use \(\pi=3.14 \) and \(\sqrt3=1.73205 \) )
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Area of equilateral
Area of sector
Find the area of shaded region in the figure, in term of \(\pi \).
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Area of square
Area of square
Area of semicircle
Area of 4 semicircle
Area of shaded region