Question 1: Find the perimeter, area and length of diagonal of a rectangle, having:

(i) length , breadth

(iii) length , breadth

(ii) length , breadth

Answer:

(i) Perimeter of a rectangle

Area of a rectangle

Length of diagonal

(ii) Perimeter of a rectangle

Area of a rectangle

Length of diagonal

(iii) Perimeter of a rectangle

Area of a rectangle

Length of diagonal

Question 2: The perimeter of a rectangle is and its length is . Find the breadth and the area of the rectangle.

Answer:

Breadth

Area of a rectangle

Question 3: The perimeter of a rectangle is and its breadth is . Find the length and the area of the rectangle.

Answer:

Length

Area of a rectangle

Question 4: The perimeter of a rectangle is and its length is . Find its breadth, area and diagonal.

Answer:

Breadth

Area of a rectangle

Length of diagonal

Question 5: The length of a rectangle is and one of its diagonals measures . Find the breadth, perimeter and area of the rectangle.

Answer:

Breadth

Perimeter of a rectangle

Area of a rectangle

Question 6: The area of a rectangle is and its length is . Find the breadth and perimeter of the rectangle.

Answer:

Breadth

Perimeter of a rectangle

Question 7: The area of a rectangle is and its breadth is . Find the length and perimeter of the rectangle.

Answer:

Length

Perimeter of a rectangle

Question 8: The sides of a rectangular park are in the ratio . If its area is , find the cost of fencing it at per meter.

Answer:

Let the length and breadth

Therefore

Therefore Length and breadth

Perimeter of a rectangle

Cost of fencing

Question 9: Find the cost of carpeting a room long and broad with a carpet broad at the rate of per meter.

Answer:

Area of a rectangle

Length of carpet required

Cost of Carpet

Question 10: A verandah long and broad is to be paved with tiles, each measuring by . Find the number of tiles needed.

Answer:

Area of a verandah

Area of a tile

Number of tiles required

Question 11: The length and breadth of a rectangular field are in the ratio and its perimeter is . Find the cost of reaping the field at per sq. meter.

Answer:

Let the length and breadth

Therefore

Therefore Length and breadth

Area of the fiels

Cost of reaping

Question 12: A room long and wide is surrounded by a verandah wide. Calculate the cost of cementing the floor of this verandah at per sq. meter.

Answer:

Area of outer perimeter

Area of inner perimeter

Therefore area of the verandah

Cost of cementing the verandah

Question 13: A rectangular grassy plot is long and broad. It has a path wide all round it on the inside. Find the cost of leveling the path at .

Answer:

Area of inner perimeter

Area of outer perimeter

Therefore area of the path

Cost of leveling the path

Question 14: A rectangular plot of land measures by . Inside the plot, a path of uniform width is to be constructed all around. The rest of the plot is to be laid with grass. Find the total expense involved in constructing the path at and laying the grass at .

Answer:

Area of inner perimeter

Area of outer perimeter

Therefore area of the path

Cost of constructing the path

Cost of laying the grass

Total cost

Question 15: A rectangular hall is long and broad. A carpet is laid inside the hall leaving all around a margin of from the walls. Find the area of the carpet and the area of the strip left uncovered. If the width of the carpet is , find its cost at the rate of per meter.

Answer:

Area of carpet

Area of outer perimeter

Therefore area of the strip left uncovered

Length of the carpet needed

Cost of laying the carpet

Total cost

Question 16: A rectangular lawn by has two roads each wide running in the middle of it, one parallel to length and the other parallel to breadth. Find the cost of graveling the roads at per sq. meter.

Answer:

Area of road running parallel to the length

Area of road running parallel to the Breadth

Area of the road to be graveled

Cost of graveling

Question 17: The length and breadth of a rectangular park are in the ratio . A wide path running all around the outside of the park has an area of . Find the dimensions of the park.

Answer:

Let the length and breadth

Area of outer perimeter

Area of inner perimeter

Therefore area of the path

Hence length

Breadth

Question 18: Find the perimeter, area and diagonal of a square each of whose sides measure: (i) (ii) (iii)

Answer:

(i) Perimeter of square

Area of square

Diagonal of square

(ii) Perimeter of square

Area of square

Diagonal of square

(iii) Perimeter of square

Area of square

Diagonal of square

Question 19: The perimeter of a square is . Find its area and the length of its diagonal.

Answer:

Perimeter

Area of square

Diagonal of square

Question 20: The diagonal of a square is . Find its area and perimeter.

Answer:

Diagonal of square:

Perimeter

Area

Question 21: The diagonal of a square is long. Find its area and perimeter.

Answer:

Diagonal of square:

Perimeter

Area

Question 22: The area of a square field is . Find its diagonal.

Answer:

Area

Diagonal

Question 23: The area of a square is . Find its perimeter and the length of its diagonal.

Answer:

Area

Perimeter

Diagonal

Question 24: A square field has an area of . Find the cost of putting the fence round it at per meter.

Answer:

Area

Perimeter

Cost of putting a fence around the field

Question 25: The cost of ploughing a square field at per square meter is . Find the cost of fencing the field at per meter.

Answer:

Area of the field

Area

Perimeter

Cost of fencing

Question 26: Find the area of the shaded region in the adjoining figure, and .

Answer:

Area of

Question 27: Find the area of the shaded region of the adjoining figure, it being given that , , , and distance between and .

Answer:

Area of the shaded region

Question 28: Find the area of the shaded region in the adjoining figure, it being given that is a square of side and .

Answer:

Area of the shaded region

Question 29: Find the area of the shaded region of each of the following:

Answer:

(i)

Shaded area

(ii)

Shaded area

(iii) Shaded area

(iv) Shaded area

(v) Shaded area