Question 1

Q1: 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....

Accepted Answer

Part 1: Area of the signal board with side 'a' Given: An equilateral triangle with side length 'a'. Sides of the triangle are $a, b, c$ such that $a = b = c = a$. To Find: The area of the triangle using Heron's formula. Formula: Area of a triangle $= \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \frac{a+b+c}...

Question 2

Q2: The triangular side walls of a flyover have been used for advertisements. The sides of the walls are $122 \mathrm{~m}, 22 \mathrm{~m}$ and $120 \mathr...

Accepted Answer

Given: Sides of the triangular wall are $a = 122 	ext{ m}$, $b = 22 	ext{ m}$, and $c = 120 	ext{ m}$. Rate of earning = ₹ 5000 per $	ext{m}^2$ per year. Duration of hire = 3 months. To Find: The rent paid by the company for 3 months. Formula: Area of a triangle by Heron's formula $= \sqrt{s(s-a...

Question 3

Q3: 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...

Accepted Answer

Given: The sides of the triangular wall are $a = 15 	ext{ m}$, $b = 11 	ext{ m}$, and $c = 6 	ext{ m}$. To Find: The area painted in colour. Formula: Area of a triangle by Heron's formula $= \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \frac{a+b+c}{2}$. Solution: First, we calculate the semi-perimeter, $...

Question 4

Q4: Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Accepted Answer

Given: Two sides of a triangle are $a = 18 	ext{ cm}$ and $b = 10 	ext{ cm}$. Perimeter of the triangle = 42 cm. To Find: The area of the triangle. Formula: Area of a triangle by Heron's formula $= \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \frac{a+b+c}{2}$. Solution: Step 1: Find the third side of the...

Question 5

Q5: Sides of a triangle are in the ratio of $12:17:25$ and its perimeter is 540 cm. Find its area.

Accepted Answer

Given: The ratio of the sides of a triangle is $12:17:25$. The perimeter of the triangle is 540 cm. To Find: The area of the triangle. Let: Let the common ratio be $x$. Then the sides of the triangle are $a = 12x$, $b = 17x$, and $c = 25x$. Solution: Step 1: Find the lengths of the sides. Perimeter...

Question 6

Q6: An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

Accepted Answer

Given: An isosceles triangle with a perimeter of 30 cm. Length of each of the equal sides is 12 cm. To Find: The area of the triangle. Solution: Step 1: Find the length of the third side. Let the sides of the triangle be $a, b,$ and $c$. Let the equal sides be $a = 12 	ext{ cm}$ and $b = 12 	ext{...

NCERT Solutions