RS Aggarwal & V Aggarwal - Mathematics

Book: RS Aggarwal & V Aggarwal - Mathematics

Chapter: 7. Areas

Subject: Mathematics - Class 9th

Q. No. 23 of Exercise 7A

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23

Find the area of the parallelogram ABCD in which AB = 14 cm, BC = 10 cm and AC = 16cm. [ Given = 1.73]

According to the question,


In order to find the area of quadrilateral ABCD,


At first,


Let us consider triangle ABC,


Say,


a = 10 cm, b = 16 cm and c = 14 cm


Now,


Semi perimeter of ΔABC, s =


=


=


= 20 cm


Now,


Area of ΔABC =


=


=


= 40√3 cm2


We know that, the diagonal of a parallelogram divides it into two triangles of equal areas.


Hence,


Area of quadrilateral ABCD = Area of ΔABC + Area of ΔACD


= Area of ΔABC × 2


= 40√3 × 2


= 80√3 cm2


= 138.4 cm2


Chapter Exercises

Exercise 7A
CCE Questions
Formative Assessment (Unit Test)

More Exercise Questions

1

Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14.5 cm.
2

The base of a triangular field is three times its altitude. If the cost of sowing the field at Rs58 per hectare is Rs783, find its base and height.
3

Find the area of triangle whose sides are 42cm,34 cm and 20cm in length. Hence find the height corresponding to the longest side.
4

Calculate the area of the triangle whose sides are 18cm, 24cm and 30 cm in length. Also, find the length of the altitude corresponding to the smallest side.
5

Find the area of a triangular field whose sides are 91m, 98m and 105m in length. Find the height corresponding to the longest side.
6

The sides of triangle are in the ratio 5 : 12 : 13 and its perimeter is 150m. Find the area of triangle.
7

The perimeter of a triangular field is 540m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle. Also, find the cost of ploughing the field at Rs. 18.80 per 10m2.
8

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 of the side measuring 154m.
9

Find the area of an isosceles triangle each of whose equal sides measures 13cm and whose base measures 20cm.
10

The base of an isosceles triangle measures 80cm and its area is 360cm2 . Find the perimeter of the triangle.
11

The perimeter of an isosceles triangle is 42cm and its base is times, each of the equal sides.

Find:


(i) The length of each side of the triangle


(ii) The area of the triangle


(iii) The height of the triangle.
12

If the area of the equilateral triangle is cm2, find its perimeter.
13

If the area of the equilateral triangle is cm2, find its height.
14

The base of a right – angles triangle measures 48cm and its hypotenuse measures 50cm. Find the area of the triangle.
15

Each side of an equilateral triangle measures 8cm. Find:

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


(ii) The height of the triangle, correct to 2 places of decimal.


Take =1.732
16

The height of an equilateral triangle measures 9 cm. Find its area, correct to 2 decimal places. Take =1.732.
17

An umbrella is made by stitching 12 triangular pieces of cloth, each measuring (50 cm x 20 cm x 50 cm). Find the area of the cloth used in it.
18

A floral design on a floor is made up of 16 tiles, each triangular in shape having sides 16 cm, 12 cm, and 20cm. Find the cost of polishing the tiles at Re 1 per sq cm.
19

Find the perimeter and area of the quadrilateral ABCD in which AB = 17cm, AD = 9cm, CD = 12cm, =900 and AC = 15cm.
20

Find the perimeter and area of the quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA = 34 cm and =900.
21

Find the area of the quadrilateral ABCD in which AD = 42 cm , = 900 and is an equilateral triangle having each side equal to 26 cm. Also, find the perimeter of the quadrilateral. [Given = 1.73]
22

Find the area of a parallelogram ABCD in which AB = 28cm, BC = 26cm and diagonal AC = 30 cm.
23

Find the area of the parallelogram ABCD in which AB = 14 cm, BC = 10 cm and AC = 16cm. [ Given = 1.73]
24

In the figure ABCD is a quadrilateral in which diagonal BD = 64 cm, AL BD and CM BD such that AL = 16.8 cm and CM = 13.2 cm. Calculate the area of the quadrilateral ABCD.

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