Area of Rectangular Shapes

Q. A momento is made as shown in the figure. Its base PBCR is silver plated from the front side. Find the area which is silver plated, where AP = AR = 7 $cm$ and PB = RC = 3 $cm$. $(Use\pi =\frac{22}{7})$

1. $8.5c{m}^2$
2. $9.5c{m}^2$
3. $10.5c{m}^2$
4. $11.5c{m}^2$

Q. 16. Four circles are inscribed in a square of side 10cm in such a way that the minimum radius is 2.5 cm.The radius of the smallest circle which touches all those four circle externally is

Q.

A triangle with integral sides has perimeter 8 units.

The area of the triangle is ______sq.units.

a) 2

b) 2*2^1\2

c) 3*2^1\2

d) 4

Q. 32. A square ABCD has each side 10 cm and two quadrant each of radius equal to side of square is inscribed in it such that some part overlap(shaded region). Find The area of shaded region (a) 2268 (b) 2520 (c) 2975 (d) 1560

Q. 14. find the area of a quadrant of a circle whose circumference is 44 cm.

Q.

From a square cardboard of side 20 cm, a circle of maximum area is cut off. What is the area of the cardboard left out after removing the circle cut off? (Take $\pi =3.14$)

1. 280 sq. cm.

2. 100 sq. cm.

3. 86 sq. cm.

4. 480 sq. cm.

Q.

Question 10
The area of an equilateral triangle ABC is 17320.5cm². 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 Fig. 12.28). Find the area of the shaded region. (Use π=3.14and√3=1.73205)

Q.

A carpenter had to make a triangle with sides 5, 6, 5 units. By mistake he made one with sides 5, 8, 5 units. The difference between their areas is:

1. 4 sq units

2. 2 sq units

3. 16 sq units

4. 0 sq units

Q. In the given figure, arcs are drawn by taking vertices $A,B$ and $C$ of an equilateral triangle of side 10 cm, to intersect the sides $BC,CAandAB$ at their respective mid-points $D,EandF$. Find the area of the shaded region.$(Use\pi =3.14)$

1. $29.25c{m}^2$
2. $39.25c{m}^2$
3. $49.25c{m}^2$
4. $59.25c{m}^2$

Q. In rectangle ABCD, G and H are trisection points of AD, and E and F are trisection points of BC. If AB360 and BC450, compute the area of PORS

Q.

OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. if OE = 2√5 cm, the area of the rectangle is

1. 

2. 

3. 

4. 

Q.

In Fig, AB and CD are two diameters of a circle (with center 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.

Q. If radius is 14 cm and angle at centre of circle is 180 degree, then length of the arc is ___ .

1. 24 cm
2. 34 cm
3. 44 cm
4. 54 cm

Q. Prove that the line segment joining the point of contact of two parallel †an gents to a circle is a diameter of the circle

Q. If the length of the rectangle is $24cm,$ breadth is $(x+5)cm$ and the area is $264c{m}^2$, then the breadth of the rectangle is

1. 11 cm
2. 6 cm
3. 5 cm
4. 3 cm

Q. In figure, AB and CD are diameters of a circle with centre O. If ∠OBD = 50⁰, find ∠AOC.

Q.

A sector is cut from a circle of radius 21 cm. The angle of the sector is 150^o. What will be the length of its arc and area.

1. 50 cm, 577 cm²

2. 60 cm, 575 cm²

3. 55 cm, 577 cm²

4. 55 cm, 577.5 cm²

Q. 14. An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45cm, find the area between the two consecutive ribs of the umbrella

Q. If radius is 14 cm and angle at centre of circle is 180 degree, then length of the arc is ___ .

1. 44 cm
2. 54 cm
3. 24 cm
4. 34 cm

Q. 38. Pqrs is a square of side 4 cm psr and qsr are two quadrants of a circles. Find the area of the circle touching a side and both the quadrants

Q. The part of a circle enclosed by two radii of a circle is called ______ of a circle.

1. sector
2. segment
3. diameter
4. area

Q. If the area of a circle is 88 sq. m, what is the area of its quadrant?

1. 22 sq. m
2. 44 sq. m
3. 55 sq. m
4. 66 sq. m

Q.

The area of a circle can be visualised by dividing the circle into equal sectors, and rearranging the sectors to form a__. The area of the rearranged figure will be equal to the area of the circle

Q. An arc is subtending at an angle 60 degree at centre. If radius is 42 cm, area of sector is:

1. 894 sq. cm
2. 904 sq. cm
3. 914 sq. cm
4. 924 sq. cm

Q.

If the edge length of a square is $a$ units, the area of the square is $\frac{a^2}{2}$ square units.

1. True

2. False

Q.

In the given figure, the sIde of the square is 28 cm, and radius of each circle is half of the length of the side of the square. O and O' are centres of the circles. Find the total area of the region shaded in green and yellow.

[2 Marks]

Q. 2. What is the area of the largest rectangle that can be placed in a semi-circle of diameter 10 cm.

Q.

In the given figure, a circle is inscribed in a trapezium of height 14 cm and lengths of parallel sides are equal to 25 cm and 40 cm. What is the area of the shaded region?

1. 509 sq cm
2. 455 sq cm
3. 154 sq cm
4. 301 sq cm

Q. A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. Find the length of the arc and the area of the sector.

Q. If the area of a circle is 88 sq. m, what is the area of its quadrant?

1. 22 sq. m
2. 44 sq. m
3. 55 sq. m
4. 66 sq. m