(B) The statement is False.According to Heron's formula, the area of a triangle with sides $a, b, c$ is given by $\sqrt{s(s-a)(s-b)(s-c)}$, where $s$

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(B) The statement is False.According to Heron's formula, the area of a triangle with sides $a, b, c$ is given by $\sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter of the triangle.The semi-perimeter $s$ is defined as $s = \frac{a+b+c}{2}$, which is equal to half of the perimeter of the triangle.In the given statement, $s$ is incorrectly defined as the perimeter of the triangle instead of the semi-perimeter.

Class 9 Mathematics Heron’s Formula Mix Examples - Heron’s Formula

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Write True or False and justify your answer.
If $a, b, c$ are the lengths of three sides of a triangle, then area of a triangle $= \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \text{perimeter of triangle}$.

A
True
B
False
C
Cannot be determined
D
None of these

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Heron’s Formula

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Mix Examples - Heron’s Formula

Write True or False and justify your answer.
The base and the corresponding altitude of a parallelogram are $10 \text{ cm}$ and $3.5 \text{ cm}$,respectively. The area of the parallelogram is $30 \text{ cm}^2$.

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The sides of a triangle measure $12 \, cm$,$16 \, cm$,and $20 \, cm$. What is the area of the triangle in $cm^2$?

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In Heron's formula,$s$ represents ............

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Find the cost of laying grass in a triangular field of sides $50 \, m$,$65 \, m$,and $65 \, m$ at the rate of $Rs \, 7$ per $m^2$ (in $Rs$).

Medium

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$A$ rhombus-shaped sheet with a perimeter of $40 \, cm$ and one diagonal of $12 \, cm$ is printed on both sides at the rate of $Rs. \, 5$ per $cm^2$. Find the total cost of printing.

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Write True or False and justify your answer.If $a, b, c$ are the lengths of three sides of a triangle, then area of a triangle $= \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \text{perimeter of triangle}$.

Similar Questions

Write True or False and justify your answer.The base and the corresponding altitude of a parallelogram are $10 \text{ cm}$ and $3.5 \text{ cm}$,respectively. The area of the parallelogram is $30 \text{ cm}^2$.

The sides of a triangle measure $12 \, cm$,$16 \, cm$,and $20 \, cm$. What is the area of the triangle in $cm^2$?

In Heron's formula,$s$ represents ............

Find the cost of laying grass in a triangular field of sides $50 \, m$,$65 \, m$,and $65 \, m$ at the rate of $Rs \, 7$ per $m^2$ (in $Rs$).

$A$ rhombus-shaped sheet with a perimeter of $40 \, cm$ and one diagonal of $12 \, cm$ is printed on both sides at the rate of $Rs. \, 5$ per $cm^2$. Find the total cost of printing.

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Write True or False and justify your answer.
If $a, b, c$ are the lengths of three sides of a triangle, then area of a triangle $= \sqrt{s(s-a)(s-b)(s-c)}$, where $s = \text{perimeter of triangle}$.

Write True or False and justify your answer.
The base and the corresponding altitude of a parallelogram are $10 \text{ cm}$ and $3.5 \text{ cm}$,respectively. The area of the parallelogram is $30 \text{ cm}^2$.