(D) Let the sides of the right-angled triangle be $a$,$b$,and $c$,where $c$ is the hypotenuse.Given: $c = 29\,cm$ and $a = 21\,cm$.Using the Pythagore

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(D) Let the sides of the right-angled triangle be $a$,$b$,and $c$,where $c$ is the hypotenuse.Given: $c = 29\,cm$ and $a = 21\,cm$.Using the Pythagorean theorem: $a^2 + b^2 = c^2$.$21^2 + b^2 = 29^2$.$441 + b^2 = 841$.$b^2 = 841 - 441 = 400$.$b = \sqrt{400} = 20\,cm$.The perimeter of the triangle is $P = a + b + c = 21 + 20 + 29 = 70\,cm$.The semi-perimeter $s$ is given by $s = \frac{P}{2} = \frac{70}{2} = 35\,cm$.

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

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In a right-angled triangle,the length of the hypotenuse is $29\,cm$ and one of the sides forming the right angle is $21\,cm$. Then,the semi-perimeter of the triangle is ............ $cm$.

A
$50$
B
$25$
C
$70$
D
$35$

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Heron’s Formula

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Mix Examples - Heron’s Formula

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State whether the following statement is True or False and justify your answer:
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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 $s = \dots \, cm$.

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In quadrilateral $ABCD$,$AB = 9 \, cm$,$BC = 13 \, cm$,$CD = 14 \, cm$,$DA = 12 \, cm$,and $BD = 15 \, cm$. Find the area of quadrilateral $ABCD$ in $cm^2$.

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Each side of an equilateral triangle measures $10\,cm$. Find the semi-perimeter of the triangle. (in $,cm$)

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In a right-angled triangle,the length of the hypotenuse is $29\,cm$ and one of the sides forming the right angle is $21\,cm$. Then,the semi-perimeter of the triangle is ............ $cm$.

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The lengths of the sides of a triangle are $13 \, cm$,$13 \, cm$,and $10 \, cm$. Find its area. Also,find the length of the altitude from the opposite vertex to the side whose length is $10 \, cm$.

State whether the following statement is True or False and justify your answer:The area of a regular hexagon of side $a$ is the sum of the areas of the five equilateral triangles with side $a$.

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 $s = \dots \, cm$.

In quadrilateral $ABCD$,$AB = 9 \, cm$,$BC = 13 \, cm$,$CD = 14 \, cm$,$DA = 12 \, cm$,and $BD = 15 \, cm$. Find the area of quadrilateral $ABCD$ in $cm^2$.

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State whether the following statement is True or False and justify your answer:
The area of a regular hexagon of side $a$ is the sum of the areas of the five equilateral triangles with side $a$.