R.S. Aggarwal solutions for Mathematics [English] Class 10 chapter 15 - Perimeter And Area of Plane Figures [Latest edition]

Find the area of triangle whose base measures 24 cm and the corresponding height measure 14.5 cm.

Find the areas of the triangle whose sides are 42 cm, 34 cm and 20 cm. Also, find the height corresponding to the longest side. 

Find the area of the triangle whose sides are 18 cm, 24 cm and 30 cm. Also find the height corresponding to the smallest side.

The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 150 m. Find the area of the triangle.  

The perimeter of a triangular field is 540 m, and its sides are in the ratio 25 : 17 : 12. Find the area of the field. Also, find the cost of ploughing the field at ₹ 40 per 100 m².

The perimeter of a right triangle is 40 cm and its hypotenuse measures 17 cm. Find the area of the triangle. 

The difference between the sides at right angles in a right-angled triangle is 7 cm. The area of the triangle is 60 cm². Find its perimeter.

The lengths of the two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is 24 cm², find the perimeter of the triangle.

Each side of an equilateral triangle is 10 cm. Find (i) the area of the triangle and (ii) the height of the triangle.

The height of an equilateral triangle is 6 cm. Find its area. [Take `sqrt(3) = 1.73`.]

If the area of an equilateral triangle is `36sqrt(3)  cm^2`, find its perimeter. 

If the area of an equilateral triangle is `81sqrt(3)  cm^2`, find its height.

The base of a right-angled triangle measures 48 cm and its hypotenuse measures 50 cm. Find the area of the triangle. 

The hypotenuse of a right-angled triangle is 65 cm and its base is 60 cm. Find the length of perpendicular and the area of the triangle. 

Find the area of a right-angled triangle, the radius of whose circumference measures 8 cm and the altitude drawn to the hypotenuse measures 6 cm. 

Find the length of the hypotenuse of an isosceles right-angled triangle whose area is 200 cm². Also, find its perimeter. [Given, `sqrt(2) = 1.41`.]

The base of an isosceles triangle measures 80 cm and its area is 360 cm². Find the perimeter of the triangle.

Each of the equal sides of an isosceles triangle measures 2 cm more than its height, and the base of the triangle measures 12 cm. Find the area of the triangle.

Find the area and perimeter of an isosceles right triangle, each of whose equal sides measures 10 cm. [Take `sqrt(2) = 1.41`.]

In the given figure, ΔABC is an equilateral triangle the length of whose side is equal to 10 cm, and ΔDBC is right-angled at D and BD = 8 cm. Find the area of the shaded region. [Take `sqrt(3) = 1.732`.]

The perimeter of a rectangular plot of land is 80 m and its breadth is 16 m. Find the length and area of the plot.

The length of a rectangular park is twice its breadth and its perimeter is 840 m. Find the area of the park.

One side of a rectangle is 12 cm long and its diagonal measures 37 cm. Find the other side and the area of the rectangle.

The area of a rectangular plot is 462 m² and its length is 28 m. Find its perimeter.

A lawn is in the form of a rectangle whose sides are in the ratio 5 : 3. The area of the lawn is 3375 m². Find the cost of fencing the lawn at ₹ 65 per metre.

A room is 16 m long and 13.5 m broad. Find the cost of covering its floor with 75-cm-wide carpet at ₹ 60 per metre. 

The floor of a rectangular hall is 24 m long and 18 m wide. How many carpets, each of length 2.5 m and breadth 80 cm, will be required to cover the floor of the hall?

A 36-m-long, 15-m-board verandah is to be paved with stones, each measuring 6 dm by 5 dm. How many stones will be required?

The area of a rectangle is 192 cm² and its perimeter is 56 cm. Find the dimensions of the rectangle. 

A rectangular park 35 m long and 18 m wide is to be covered with grass, leaving 2.5 m uncovered all around it. Find the area to be laid with grass.

A rectangular plot measures 125 m by 78 m. It has a gravel path 3 m wide all around on the outside. Find the area of the path and the cost of gravelling it at ₹ 75 per m². 

A footpath of uniform width runs all around the inside of a rectangular field 54 m long and 35 m wide. If the area of the path is 420 m², find the width of the path.

A carpet is laid on the floor of a room 8 m by 5 m. There is a border of constant width all around the carpet. If the area of the border is 12 m², find its width.

The length and the breadth of a rectangular garden are in the ratio 9 : 5. A path 3.5 m wide, running all around inside it has an area of 1911 m². Find the dimensions of the garden.

A room 4.9 m long and 3.5 m board is covered with carpet, leaving an uncovered margin of 25 cm all around the room. If the breadth of the carpet is 80 cm, find its cost at ₹ 80 per metre.

In a rectangular park of dimensions 50 m × 40 m, a rectangular pond is constructed so that the area of grass strip of uniform width surrounding the pond would be 1184 m². Find the length and breadth of the pond.

A 80 m by 64 m rectangular lawn has two roads, each 5 m wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of gravelling the roads at ₹ 40 per m^2.

The dimensions of a room are 14 m × 10 m × 6.5 m. There are two doors and 4 windows in the room. Each door measures 2.5 m × 1.2 m and each window measures 15 m × 1 m. Find the cost of painting the four walls of the room at ₹ 35 per m².

The cost of painting the four walls of a room 12 m long at ₹ 30 per m² is ₹ 7560 and the cost of covering the floor with mat at ₹ 25 per m² is ₹ 2700. Find the dimensions of the room. 

Find the area and perimeter of a square plot of land whose diagonal is 24 m long. [Take `sqrt(2) = 1.41`.]

Find the length of the diagonal of a square whose area is 128 cm². Also, find its perimeter.

The area of a square filed is 8 hectares. How long would a man take to cross it diagonally by walking at the rate of 4 km per hour?

The cost of harvesting a square field at ₹ 900 per hectare is ₹ 8100. Find the cost of putting a fence around it at ₹ 18 per metre. 

The cost of fencing a square lawn at ₹ 14 per metre is ₹ 28000. Find the cost of mowing the lawn at ₹ 54 per 100 m².

In the given figure, ABCD is a quadrilateral in which diagonal BD = 24 cm, AL ⊥ BD  and CM ⊥ BD such that AL = 9 cm and CM = 12 cm. Calculate the area of the quadrilateral.  

Find the area of the quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and ΔBCD is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral. [Given, `sqrt(3) = 1.73`.]

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ACB = 90° and AC = 15 cm. 

Find the area of the quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm. 

Find the area of a parallelogram with base equal to 25 cm and the corresponding height measuring 16.8 cm. 

The adjacent sides of a parallelogram are 32 cm and 24 cm. If the distance between the longer sides is 17.4 cm, find the distance between the shorter sides. 

The area of a parallelogram is 392 m². If its altitude is twice the corresponding base, determine the base and the altitude.

The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram. 

Find the area of the rhombus, the length of whose diagonals are 30 cm and 16 cm. Also, find the perimeter of the rhombus. 

The perimeter of a rhombus is 60 cm. If one of its diagonals is 18 cm long, find

(i) the length of the other diagonal, and

(ii) the area of the rhombus.

The area of a rhombus is 480 cm², and one of its diagonals measures 48 cm. Find

(i) the length of the other diagonal,

(ii) the length of each of its sides, and

(iii) its perimeter.

The parallel sides of a trapezium are 12 cm and 9 cm and the distance between them is 8 cm. Find the area of the trapezium.

The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is 640 m², find the depth of the canal.

Find the area of a trapezium whose parallel sides are 11 m and 25 m long, and the nonparallel sides are 15 m and 13 m long.

The length of a rectangular hall is 5 m more than its breadth. If the area of the hall is 750 m² then its length is ______.

The length of a rectangular field is 23 m more than its breadth. If the perimeter of the field is 206 m then its area is ______.

The length of a rectangular field is 12 m and the length of its diagonal is 15 m. The area of the field is ______.

The cost of carpeting a room 15 m long with a carpet 75 cm wide, at ₹ 70 per metre, is ₹ 8400. The width of the room is ______.

The length of a rectangle is thrice its breadth and the length of its diagonal is `8sqrt(10)` cm. The perimeter of the rectangle is ______.

On increasing the length of a rectangle by 20% and decreasing its breadth by 20%, what is the change in its area?

A rectangular ground 80 m × 50 m has a path 1 m wide outside around it. The area of the path is ______.

The length of the diagonal of a square is `10sqrt(2)` cm. Its area is ______.

The area of a square field is 6050 m². The length of its diagonal is ______.

The area of a square field is 0.5 hectare. The length of its diagonal is ______.

The area of an equilateral triangle is `4sqrt(3)` cm². Its perimeter is ______.

Each side of an equilateral triangle is 8 cm. Its area is ______.

Each side of an equilateral triangle is `6sqrt(3)` cm. The altitude of the triangle is ______.

The height of an equilateral triangle is `3sqrt(3)` cm. Its area is ______.

The base and height of a triangle are in the ratio 3 : 4 and its area 216 cm². The height of the triangle is ______.

The lengths of the sides of a triangular field are 20 m, 21 m and 29 m. The cost of cultivating the field at ₹ 9 per m² is ______.

The side of a square is equal to the side of an equilateral triangle. The ratio of their areas is ______.

The side of an equilateral triangle is equal to the radius of a circle whose area is 154 cm². The area of the triangle is ______.

The area of a rhombus is 480 cm² and the length of one of its diagonals is 20 cm. The length of each side of the rhombus is ______.

One side of a rhombus is 20 cm long and one of its diagonals measures 24 cm. The area of the rhombus is ______.

In the given figure ABDC is a quadrilateral in which ∠ABC = 90°, ∠BDC = 90°, AC = 17 cm, BC = 15 cm, BD = 12 cm and CD = 9 cm. The area of quad. ABDC is ______.

In the given figure ABCD is a trapezium in which AB = 40 m, BC = 15 m, CD = 28 m, AD = 9 m and CE ⊥ AB. The area of trap. ABCD is ______.

The sides of a triangle are in the ratio 12 : 14 : 25 and its perimeter is 25.5 cm. The largest side of the triangle is ______.

The parallel sides of a trapezium are 9.7 cm and 6.3 cm, and the distance between them is 6.5 cm. The area of the trapezium is ______.

Find the area of an equilateral triangle having each side of length 10 cm. [Take `sqrt(3) = 1.732`.]

Find the area of an isosceles triangle each of whose equal sides is 13 cm and whose base is 24 cm.

The longer side of a rectangular hall is 24 m and the length of its diagonal is 26 m. Find the area of the hall.

The length of the diagonal of a square is 24 cm. Find its area.

Find the area of a rhombus whose diagonals are 48 cm and 20 cm long.

Find the area of a triangle whose sides are 42 cm, 34 cm and 20 cm.

A lawn is in the form of a rectangle whose sides are in the ratio 5 : 3 and its area is 3375 m². Find the cost of fencing the lawn at ₹ 20 per metre.

Find the area of a trapezium whose parallel sides are 11 cm and 25 cm long and nonparallel sides are 15 cm and 13 cm.

The adjacent sides of a ||gm ABCD measure 34 cm and 20 cm and the diagonal AC is 42 cm long. Find the area of the ||gm.

The cost of fencing a square lawn at ₹ 14 per metre is ₹ 2800. Find the cost of mowing the lawn at ₹ 54 per 100 m².

Find the area of quad. ABCD in which AB = 42 cm, BC = 21 cm, CD =  29 cm, DA = 34 cm and diag. BD = 20 cm.

A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 120 m and 44 m. If one of the sides of the ||gm is 66 m long, find its corresponding altitude.

The diagonals of a rhombus are 48 cm and 20 cm long. Find the perimeter of the rhombus.

The adjacent sides of a parallelogram are 36 cm and 27 cm in length. If the distance between the shorter sides is 12 cm, find the distanceе between the longer sides.

In a four-sided field, the length of the longer diagonal is 128 m. The lengths of perpendiculars from the opposite vertices upon this diagonal are 22.7 m and 17.3 m. Find the area of the field.