Gujarat Board Textbook Solutions Class 9 Maths Chapter 12 Heron’s Formula
GSEB Solutions Class 9 Maths Chapter 12 Heron’s Formula
Ex 12.1
Question 1.
A traffic signal board, indicating ‘SCHOOL AHEAD’ is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Solution:
According to the question, semi-perimeter of ΔABC
Question 2.
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m. The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Question 3.
There is a slide in a park. One of its side walls has been painted in some color with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m, and 6 m, find the area painted in color.
Given, a = 15m, b = 11 m, c = 6m.
Question 4.
Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Solution:
Given, a = 18 cm, b = 10 cm, perimeter =42 cm.
a + b + c = 42
18 + 10 + c = 42
28 + c = 42
c = 14cm
Question 5.
Sides of a triangle are in the ratio of 12: 17 : 25 and its perimeter is 540 cm. Find its area.
Solution:
Let the sides of a triangle be 12x cm, 17x cm and 25x cm.
Perimeter = 12x + 17x + 25x = 54x cm
54x = 540
x = 10
Question 6.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Solution:
Given, a = 12 cm, b = 12 cm, Perimeter = 30 cm
a + b + c = 30
12 + 12 + c = 30
c = 30 – 24 = 6cm
Ex 12.2
Question 1.
A park in the shape of a quadrilateral ABCD, has ∠C = 90°,AB = 9m, BC = 12m,CD = 5m and AD = 8 m. How much area does it occupy?
Solution:
Join BD.
Area of right triangle BCD
∴ Area of the quadrilateral ΔBCD
= Area of ΔBCD + Area of ΔABD
= 30 m2 + 35.5 m2
= 65.5 m2 (approx.)
Hence, the park occupies the area 65.5 m2 (approx.).
Question 2.
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC =5cm.
Solution:
For ΔABC
a = 4cm, b = 5cm, c = 3cm
∴ a2 + c2 = b2
= 2 x 4.6 cm2 (approx.)
= 9.2 cm2 (approx.)
∴ Area of the quadrilateral ABCD
= Area of ΔABC + Area of ΔACD
= 6 cm2 + 9.2 cm2
= 15.2 cm2 (approx.)
∴ Area of the quadrilateral ABCD
= Area of ÊABC + Area of ΔACD
= 6 cm2 + 9.2 cm2
= 15.2 cm2 (approx.)
Question 3.
Radha made a picture of an aeroplane with colored paper as shown in figure. Find the total area of the paper used.
Question 4.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm, and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Solution:
For triangle
Question 5.
A rhombus-shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
For ΔABC
a = 30m, b = 48m, c = 30m
Question 6.
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
Question 7.
A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and side 6 cm each is to be made of three different shades as shown in figure. How much paper of each shade has been used in it?
Question 8.
A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of 50 paise per cm2.
Question 9.
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The nonparallel sides are 14 m and 13 m. Find the area of the field.
Solution:
Let the given field be in the shape of a trapezium ABCD in which AB = 25 m, CD = 10 m, BC = 13m and AD = 14m. FromD,drawDEIIBC meeting AB at E. Also, draw DE .L AB.
