Question

if hypernews and base of a right angle are 10cm and 8cm are respectievly find its area.​

Answer 1

Answer:

Step-by-step explanation:

$\frak Given = \begin{cases} &\sf{Hypotenuse\ of\ the\ right\ angled\ triangle\ =\ 10cm.} \\ &\sf{Base\ of\ the\ right\ angled\ triangle\ =\ 8cm.} \end{cases}$

To find:- We have to find the area of the right angled triangle ?

☯️ In this question, the height of the triangle is not given. So, to find the area of the triangle first let us find out the height.

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$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf : \implies {Pythagoras\ Theorem\ =\ a^2\ +\ b^2\ =\ c^2.}$

Here:-

a, is for height.

b, is for base.

c, is for hypotenuse.

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$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {a^2\ +\ b^2\ =\ c^2} \\ \\ \sf : \implies {a^2\ +\ 8^2\ =\ 10^2} \\ \\ \sf : \implies {a^2\ +\ 64\ =\ 100} \\ \\ \sf : \implies {a^2\ =\ 100\ -\ 64} \\ \\ \sf : \implies {a^2\ =\ 36} \\ \\ \sf : \implies {a\ =\ \sqrt{36}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf a\ =\ 6cm.}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ required\ height\ of\ the\ triangle\ is\ 6cm.}}$

● Now, finding the area of the triangle:-

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$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf : \implies {Area\ of\ triangle\ =\ \dfrac{1}{2}\ \times\ b\ \times\ h.}$

Here:-

b, is for base.

h, is for height.

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$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {Area\ =\ \dfrac{1}{2}\ \times\ b\ \times\ h} \\ \\ \sf : \implies {\dfrac{1}{\cancel 2}\ \times\ \cancel 8\ \times\ 6} \\ \\ \sf : \implies {4\ \times\ 6} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf Area\ =\ 24cm^2.}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ required\ area\ is\ 24cm^2.}}$