(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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Class 9

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Heron’s Formula

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Mix Examples - Heron’s Formula

$PQRS$ is a square. If $PR = 10 \, cm$,then the area of $PQRS = \dots \, cm^2$.

Medium

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The sides of a triangle are $a \, cm$,$b \, cm$,and $c \, cm$. Also,its semi-perimeter is $s \, cm$. If $s - a = 10 \, cm$,$s - b = 15 \, cm$,and $s - c = 12 \, cm$,then $s = \dots \, cm$.

Medium

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Find the area of the triangle with the side lengths $51 \, cm$,$52 \, cm$,and $101 \, cm$. (in $, cm^2$)

Medium

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Area of a trapezium $=$ .........

Easy

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The sides of a quadrilateral $ABCD$ are $6 \, cm$,$8 \, cm$,$12 \, cm$,and $14 \, cm$ (taken in order) respectively,and the angle between the first two sides is a right angle. Find its area in $cm^2$.

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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

$PQRS$ is a square. If $PR = 10 \, cm$,then the area of $PQRS = \dots \, cm^2$.

The sides of a triangle are $a \, cm$,$b \, cm$,and $c \, cm$. Also,its semi-perimeter is $s \, cm$. If $s - a = 10 \, cm$,$s - b = 15 \, cm$,and $s - c = 12 \, cm$,then $s = \dots \, cm$.

Find the area of the triangle with the side lengths $51 \, cm$,$52 \, cm$,and $101 \, cm$. (in $, cm^2$)

Area of a trapezium $=$ .........

The sides of a quadrilateral $ABCD$ are $6 \, cm$,$8 \, cm$,$12 \, cm$,and $14 \, cm$ (taken in order) respectively,and the angle between the first two sides is a right angle. Find its area in $cm^2$.

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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 $s = \text{perimeter of triangle}$.