Question

If hypotenuse of right angle isosceles triangle is 4 √2 cm. Find its area.
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Answer 1

Answer:

Area = 8 cm^2  

Step-by-step explanation:

Given , Hypotenuse = 4$\sqrt{2}$

since it is a right angle triangle, h^2 = p^2 + b^2

and since it is a isosceles triangle ,perpendicular = base

h^2 = P^2 + p^2     [Since,perpendicular = base]

h^2 = 2 * (p^2)

(4$\sqrt{2}$)^2 = 2 * (p^2)

16 * 2 = 2 * (p^2)

16 = p^2

Therefore, p = 4 and b = 4

Area = base * height / 2

        = 4 * 4 / 2

        = 16 / 2

        = 8 cm^2  

Answer 2

$\bigstar \underline{\underline{\large{\mathfrak{Given:-}}}}$

• Triangle is right angled isosecles.
• Length of hypotenuse=4√2 cm.

$\bigstar \underline{\underline{\large{\mathfrak{To\ find:-}}}}$

• Area of triangle.

$\bigstar \underline{\underline{\large{\mathfrak{Solution:-}}}}$

❥ For an isosceles triangle, 2 sides are equal.

Let Length of  opposite side & adjacent sides of the given triangle be x.

Given the hypotenuse is  4 √2 cm.

By pythagoras theorem :

❥(Hypotenuse)²=(opp side)²+(adj side)²

$:\implies \sf (4\sqrt{2} )^2=x^2 + x^2\\\\:\implies \sf 16(2)=2x^2 \\\\:\implies 16 = x^2\\\\:\implies x=\sqrt{16} \\\\:\implies \orange{\bold{x= 4.}}$

Hence , the length's of opposite side & adjacent side is 4cm.

Now,

---------------------------------------

❥Area of triangle=1/2×b×h

---------------------------------------

Where ,

=> b = base of triangle ,

=> h = height of triangle

We found out that the base & height of triangle is 4cm.

Substituting values in Area formula :

$\mapsto \sf Area=\frac{1}{2} bh\\\\:\implies \frac{1}{2} \times (x) \times (x)\\\\:\implies \frac{1}{2}\times (4)^2\\\\:\implies \frac{1}{2} \times16=\frac{16}{2} = \bold{ 8cm^2.}$

$\therefore \orange{\boxed{\boxed{\sf Area\ of\ triangle=8cm^2.}}}$

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HOPE IT HELPS !