R s aggarwal solutions mathematics class 9 Solutions for Chapter 14 areas of triangles and quadrilaterals

Exercises in Chapter 14 areas of triangles and quadrilaterals Grade 9

Areas Of Triangles And Quadrilaterals Exercise 14

Questions in Areas Of Triangles And Quadrilaterals Exercise 14

The base of a triangular field is three times its altitude. If the cost of sowing the field at ₹ 58 per hectare is ₹ 783, find its base and height.

Find the area of the triangle whose sides are 42cm, 34cm, and 20cm in length. Hence, find the height corresponding to the longest side.

Calculate the area of the triangle whose sides are 18cm, 24cm, and 30cm in length. Also, find the length of the altitude corresponding to the smallest side.

Find the area of a triangular field whose sides are 91m, 98m, and 105m in length. Find the height corresponding to the longest sides

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

The perimeter of a triangular field is 540m and its sides are in the ratio 25: 17: 12. Find the area of the field. Also, find the cost of plowing the field at ₹ 5 per m2.

Two sides of a triangular field are 85m and 154m in length and its perimeter is 324m. Find

(i) the area of the field and

(ii) the length of the perpendicular from the opposite vertex on the side measuring 154m.

Find the area of an isosceles triangle each of whose equal sides measures 13cm and whose base measures 20cm.

The base of an isosceles triangle measures 80cm and its area is $360\mathrm{cm}^2$ . Find the perimeter of the triangle.

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

The perimeter of an isosceles triangle is 32cm. The ratio of the equal side to its base is 3:2. Find the area of the triangle

The perimeter of a triangle is 50cm. One side of the triangle is 4 cm longer than the smallest side and the third side is 6cm less than twice the smallest side. Find the area of the triangle.

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13m, 14m, 15m. The advertisements yield an earning of ₹ 2000 per m2 a year. A company hired one of its walls for 6 months. How much rent did it pay?

The perimeter of an isosceles triangle is 42cm and its base is 1 ½ time each of the equal sides. Find

(i) the length of each side of the triangle,

(ii) the area of the triangle, and

(iii) the height of the triangle. (Given, √7 = 2.64.)

If the area of an equilateral triangle is 36√3 cm2, find its perimeter.

If the area of an equilateral triangle is $81\sqrt{3}\mathrm{cm}^2$ , find its height.

Each side of an equilateral triangle measures 8cm. Find

(i) the area of the triangle, correct to 2 places of decimal and

(ii) the height of the triangle, correct to 2 places of decimal. (Take √3 = 1.732)

The height of an equilateral triangle measures 9cm. Find its area, correct to 2 places of decimal. (Take √3 = 1.732)

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

Find the area of the shaded region in the figure given below.

The sides of a quadrilateral ABCD taken in order are 6cm, 8cm, 12 cm, and 14cm respectively and the angle between the first two sides is a right angle. Find its area. (Given, √6 = 2.45.)

Find the perimeter and area of a quadrilateral ABCD in which BC = 12 cm, CD = 9 cm, BD = 15cm, DA = 17 cm and ∠ ABD = $90^{\circ}$