Area of Square & Rectangle

Q.

In a building, there are $24$ cylindrical pillars. For each pillar, the radius is $28m$ and the height is $4m.$ Find the total cost of painting the curved surface area of the pillars at the rate of $Rs.8$ per metre square

Q. A closed cylindrical tank of radius 7m and height 3m is made from a sheet of metal .find the area of metal required.

Q.

The perimeter of a square is 36 cm; find its area.

Q.

The diagonal of a square is $12cm$ long. find its area and length of one side.

Q. 12 painters can paint a wall of 180 m long in 3 days. How many painters are required to paint 200 m long wall in 5 days?

Q.

Find the area of a regular hexagon ABCDEF in which each side mesures 13 cm and whose height is 23 cm, as shown in the given figure.

Q. The shape of a farm is a quadrilateral. Measurements taken of the farm, by naming its corners as P, Q, R, S in order are as follows. l(PQ) = 170 m, l(QR) = 250 m, l(RS) = 100 m, l(PS) = 240 m, l(PR) = 260 m.
Find the area of the field in hectare (1 hectare = 10, 000 sq.m)

Q. A copper wire of length 44 cm is to be bent into a square and a circle. Which will have a larger area?

Q.

A wire, when bent in the form of a square, encloses an area of $196c{m}^2$. If the same wire is bent to form a circle, find the area of the circle.

Q.

The perimeter of a rectangle is $46m$ and its length is $15m.$ Find its:

(i) breadth (ii) area (iii) diagonal.

Q.

Find the perimeter and area of a square of side $3cm.$

Q. The breadth of a rectangular garden is $\frac{2}{3}$ of its length. If its perimeter is 40 m, find its length?

1. 16 m
2. 12 m
3. 6 m
4. 10 m

Q.

The ratio of two numbers is $2:3$. If $2$ is subtracted from first and $8$ from second, the ratio becomes reciprocal of the original ratio. Find the numbers.

Q.

Find the length and perimeter of a rectangle, whose: area $=120c{m}^2$ and breadth =8 cm

Q.

The area of a small rectangular plot is $84m^2$. If the difference between its length and the breadth is 5 m; find its pereimeter.

Q.

The diagonal of a rectangle is 34 cm. If its breadth is 16 cm; find its:

(i) length (ii) area

Q.

A wire, when bent in the form of a square, encloses an area of 484 cm2. Find :

(i) one side of the square

(ii) length of the wire

(iii) the largest area enclosed, if the same wire is bent to form a circle.

Q.

The area of a square is $169c{m}^2$. Find its :

(i) one side (ii) perimeter

Q.

Laim tells his son that i was your present age when you were born
If Laim is 36 now how old was his son five years ago.

Q. The diameter and height of a cylindrical tank are 7m and 9m respectively . If the inner side of the tank is to be painted all over what will it cost at ₹35 per square metre ?

Q.

A rectangular field is 30 m in length and 22 m in width. Two mutually perpendicular roads, each 2.5 m wide, are drawn inside the field so that one road is parallel to the lenath of the field and the other road is parallel to its width. Calculate the area of the corssroads.

Q.

Question 93

Find the area of the shaded portion in the given figure.

Q.

Each side of a rectangle is doubled. Find the ratio between :

(i) perimeters of the original rectangle and the resulting rectangle.

(ii) areas of the original rectangle and the resulting rectangle.

Q.

In each of the following cases ABCD is a square and PQRS is a rectangle. Find, in each case, the area of the shaded portion.

(All measurements are in metre)

Q.

Question 117

Solve the following question:

Find the area of a square field, if its perimeter is 96 m.

Q.

Find the area of the square whose side is : $2.5\text{cm}$

Q. Two fields have same perimeter. One is a rectangle of length 70 m and another is a square of side 51 m. Which field has greater area and what is its value?

1. Rectangular field, $2548{\text{m}}^2$
2. Square field, $2601{\text{m}}^2$
3. Both Square and Rectangular field have same area
4. Rectangular field, $2240{\text{m}}^2$

Q.

Find the perimeter of a square whose area is 1.69 $m^2$.

Q.

A path of uniform width, 3 m, runs around the outside of a square field of side 21 m. Find the area of the path.

Q.

A photograph is $16$ inches long and has an area of $(16x+96)$ square inches. A custom-made frame is $2$ inches wide and costs $\$0.50$ per square inch. Write an expression that represents the cost of the frame