Statistics

Sponsor Area

Question

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

'a' = a
'b' = a
'c' = a
$therefore space space space space space space space space straight s space equals space fraction numerator apostrophe straight a apostrophe plus apostrophe straight b apostrophe plus apostrophe straight c apostrophe over denominator 2 end fraction equals fraction numerator straight a plus straight a plus straight a plus over denominator 2 end fraction equals fraction numerator 3 straight a over denominator 2 end fraction$
Area of the signal board
$equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root equals square root of fraction numerator 3 straight a over denominator 2 end fraction open parentheses fraction numerator 3 straight a over denominator 2 end fraction minus straight a close parentheses open parentheses fraction numerator 3 straight a over denominator 2 end fraction minus straight a close parentheses open parentheses fraction numerator 3 straight a over denominator 2 end fraction minus straight a close parentheses end root square root of fraction numerator 3 straight a over denominator 2 end fraction open parentheses straight a over 2 close parentheses open parentheses straight a over 2 close parentheses open parentheses straight a over 2 close parentheses end root equals square root of fraction numerator 3 straight a to the power of 4 over denominator 16 end fraction end root equals fraction numerator square root of 3 over denominator 4 end fraction straight a squared$
Perimeter = 180 cm
$rightwards double arrow$ 'a' + 'b' + 'c' = 180
$rightwards double arrow$ a + a + a = 180
$rightwards double arrow$ 3a = 180
$rightwards double arrow space space space space space space space straight a space equals space 180 over 3$
$rightwards double arrow space space space$ a = 60 cm
$therefore$ Area of the signal board $equals fraction numerator square root of 3 over denominator 4 end fraction straight a squared$
$equals fraction numerator square root of 3 over denominator 4 end fraction left parenthesis 60 right parenthesis squared equals 900 square root of 3 space cm squared$
Alternatively,
$space space space space space straight s space equals fraction numerator 3 straight a over denominator 2 end fraction equals 3 over 2 left parenthesis 60 right parenthesis equals 90 space cm$
Area of the signal board
$equals square root of straight s left parenthesis straight s minus straight a left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root equals square root of 90 left parenthesis 90 minus 60 right parenthesis left parenthesis 90 minus 60 right parenthesis left parenthesis 90 minus 60 right parenthesis end root equals space square root of 90 left parenthesis 30 right parenthesis left parenthesis 30 right parenthesis left parenthesis 30 right parenthesis end root equals 900 square root of 3 space cm squared$

Sponsor Area

Question

Wired Faculty App

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 (see figure). The advertisements yield an earning of र5000 per m² per year. A company hired one of its walls for 3 months. How much rent did it pay?

Solution

a =122 m
b = 22 m
c = 120 m
$therefore space space space space straight s equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction equals fraction numerator 122 plus 22 plus 120 over denominator 2 end fraction straight m space space space space space space space space equals space 264 over 2 space space straight m space equals space 132 space straight m$

1 year =12 months
V Rent for 12 months per m²= र 5000

$therefore space$ Rent for 1 month per m² = र $5000 over 2$
$therefore$ Rent for 3 months of 1320 m²
$equals space र 5000 over 12 cross times 3 equals space र space 1250$

$therefore space space$ Rent for 3 months of 1320 m²
= र (1250 x 1320)
= र 1650000.

Question

Wired Faculty App

There is a slide in a park. One of its side walls has been painted in some colour 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 colour.

Solution

a = 15 m
b = 11 m
c = 6 m
$therefore space space space space space straight s equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction space space space space space space space space space equals space fraction numerator 15 plus 11 plus 6 over denominator 2 end fraction straight m space equals space 16 space straight m$
$therefore$ Area painted in colour
$equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b left parenthesis straight s minus straight c right parenthesis end root equals square root of 16 left parenthesis 16 minus 15 right parenthesis left parenthesis 16 minus 11 right parenthesis left parenthesis 16 minus 6 right parenthesis end root space straight m squared equals space square root of 16 left parenthesis 1 right parenthesis left parenthesis 5 right parenthesis left parenthesis 10 right parenthesis end root space straight m squared space equals space 20 square root of 2 space straight m squared.$

Question

Wired Faculty App

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Solution

a = 18 cm
b = 10 cm Perimeter - 42 cm
⇒ a + b + c = 42
⇒ 18 + 10 + c = 42
⇒ 28 + c = 42
⇒ c = 42 – 28
⇒ c = 14 cm
$space space space space space space space space space space space space space straight s equals 42 over 2 equals 21 space cm$
$therefore space space space space space$ Area of the triangle
$equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root equals square root of 21 left parenthesis 21 minus 18 right parenthesis left parenthesis 21 minus 10 right parenthesis left parenthesis 21 minus 14 right parenthesis end root equals square root of 21 left parenthesis 3 right parenthesis left parenthesis 11 right parenthesis left parenthesis 7 right parenthesis end root equals space square root of left parenthesis 7 right parenthesis left parenthesis 3 right parenthesis left parenthesis 3 right parenthesis left parenthesis 11 right parenthesis left parenthesis 7 right parenthesis end root equals space left parenthesis 7 right parenthesis left parenthesis 3 right parenthesis square root of 11 equals 21 square root of 11 space cm squared$

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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?

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 (see figure). The advertisements yield an earning of र5000 per m² per year. A company hired one of its walls for 3 months. How much rent did it pay?

There is a slide in a park. One of its side walls has been painted in some colour 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 colour.

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

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NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

WhatsApp Group

Download Android App

Ncert Book Download

Statistics

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?

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 (see figure). The advertisements yield an earning of र5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?

There is a slide in a park. One of its side walls has been painted in some colour 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 colour.

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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 (see figure). The advertisements yield an earning of र5000 per m² per year. A company hired one of its walls for 3 months. How much rent did it pay?