Identifying Shapes and Areas of Different Regular Figures

Q. The area of an equilateral triangle with side $2\sqrt{3}cm$ is ________.

1. $5.196c{m}^2$
2. $0.866c{m}^2$
3. $3.496c{m}^2$
4. $1.732c{m}^2$

Q. Question 1
A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?

Q. Question 3
The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 - (3.5 + 3.5 meters)]

Q.

A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm.How many such tiles are required to cover a floor of area 1080 $m^2$ ?

Q. Question 5
An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, the circumference of a circle can be obtained by using the expression $c=2\pi r$, where r is the radius of the circle.

Q.

A rectangular grassy plot is $112m$ long and $78m$ broad. It has a travel path $2.5m$ wide all around it on the sides. Find the area of the path.

Q. The length of each side of an equilateral triangle having an area of $9\sqrt{3}c{m}^2$ is

1. 36 cm
2. 4 cm
3. 6 cm
4. 8 cm

Q. Question 2
Mrs Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot with the dimensions $20m\times 15m$. A garden is developed around the house.Find the total cost of developing a garden around the house at the rate of 55 per $m^2$.

Q.

Find the area of an equilateral triangle of side 10 cm.

1. $18\sqrt{3}c{m}^2$

2. $25\sqrt{3}c{m}^2$

3. $12\sqrt{3}c{m}^2$

4. $27\sqrt{3}c{m}^2$

Q. Find the area of an equilateral triangle of side 6 cm.

1. None of these
2. $18\sqrt{3}$ $c{m}^2$
3. $9\sqrt{3}$ $c{m}^2$
4. $12\sqrt{3}$ $c{m}^2$

Q. Two adjacent sides of a parallelogram is 12 and 8 cm. If the length of the altitude corresponding to the side 12 cm is 6 cm find the length of the altitude corresponding the other pair of the side

Q. If the radii of two concentric circles are 15 cm and 13 cm, respectively, then the area of the circulating ring in sq. cm is ___.

1. 180 sq.cm
2. 200 sq.cm
3. 176 sq.cm
4. 178 sq.cm

Q.

Find the area of square if its perimeter is $4m.$

Q.

A circle of maximum possible size is cut from a square sheet of board. Subsequently, a square of maximum possible size is cut from the resultant circle. What will be the area of the final square?

1. $\frac{3}{4}$ of the original square

2. $\frac{1}{2}$ of the original square

3. $\frac{1}{4}$ of the original square

4. $\frac{2}{3}$ of the original square.

Q. Question 4
A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area $1080m^2$? [If required, you can split the tiles in whatever way you want to fill up the corners]

Q.

Find the area of the Figure in square cm, correct to one place of decimal. $(Take\pi =\frac{22}{7})$

Q.

One can of frosting covers about $280squareinches$. Is one can of frosting enough to frost the cake? Explain.

Q.

Question 104

Below are the drawings of cross sections of two different pipes used to fill swimming pools. Figure A is a combination of 2 pipes each having a radius of 8 cm. Figure B is a pipe having a radius of 15 cm. If the force of the flow of water coming out of the pipes is the same in both the cases, which will fill the swimming pool faster?

Q.

A plot is in the form of a rectangle ABCD having semi-circle on BC as shown in Fig.If AB=60 m and BC=28 m, find the area of the plot.

Q. The length of the diagonal of a square is 6 cm, what is its area?

1. 18 sq cm
2. 36 sq cm
3. 9 sq cm
4. 12 sq cm

Q.

What will be the ratio of the areas of squares, when the diagonal of one square is twice of the other.

1. 4:1

2. 1:3

3. 3:1

4. 5:1

Q. The area of a square playground is 291.0436 square metres. Find the length of each side of the play ground. [4 MARKS]

Q.

There are 3 semicircles in the given figure. AB = 14 cm and C is the midpoint of AB. Find the perimeter and area of the figure. [3 MARKS]

Q. A path of uniform width, 2.5 m, runs around the inside of a rectangular field 30 m by 27 m. Find the area of the path.

Q.

Question 100

A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in the figure below.

Does the perimeter change? If it does change, by how much does it increase or decrease?

Q. The front wheels of a wagon are 2 π metre in circumference and the back wheels are 3π metre in circumference. When the front wheels have made 10 more revolutions than the back wheels, how many metres has the wagon travelled?

1. $16\pi$
2. $20\pi$
3. $60\pi$
4. $23\pi$

Q. The length of diagonal of a square whose area is 16900 $m^2$ is ___ .

1. $130\sqrt{2}m$
   
2. 144 m
3. 169 m
   
4. 30 m

Q.

A rectangular piece is 20 m long and 15 m wide.From its four corners, quadrants of radii 3.5 have been cut.Find the area of the remaining part.

Q.

Question 18

The area of a parallelogram is $60c{m}^2$ and one of its altitude is 5 cm. The length of its corresponding side is

(a) 12 cm
(b) 6 cm
(c) 4 cm
(d) 2 cm

Q. Question 1
A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?