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As it's an isosceles right triangle, the right angle is the angle between the two sides of equal length.

Using Pythagoras, the lengths of these sides, and hence the area can be found:

2 x side2 = (6√2)2

⇒ side2 = 62

⇒ side = 6

⇒ area = 1/2 x 6 x 6

= 18 sq units.

Q: How do you find the area of an isosceles right triangle with hypotenuse 6sqrt2?

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The hypotenuse of an isosceles right triangle is 13 centimeters long. How long are its sides?

An isosceles right triangle will always have its shorter sides of the same length, and the hypotenuse will always be this length times sin(45o) or times the square root of 0.5.

If the hypotenuse is the square root of three, then the legs are (root 6)/2. If the hypotenuse is 12, then the legs are 6(root 2). This is because, for any given right isosceles triangle, the length of the hypotenuse x is root two times the length of the legs.

Area of the right isosceles triangle: 0.5*16*16 = 128 square units

It would be an isosceles right triangle. The two sides that aren't the hypotenuse are equal, with lengths of 16.971 (rounded) .

Related questions

Only a right triangle has a hypotenuse. An isosceles triangle can be a right triangle but it doesn't have to be. If it's not, then it doesn't have a hypotenuse.

The hypotenuse of an isosceles right triangle is 13 centimeters long. How long are its sides?

Yes if the isosceles triangle is a right isosceles triangle because that leg opposite the hypotenuse is the height

An Isosceles right triangle. If the length of either of the two sides is N then the hypotenuse is N times the square root of 2. an isosceles right triangle can not be an equilateral triangle since the hypotenuse can not be the same size as the other two sides..

Isosceles.

An isosceles right triangle will always have its shorter sides of the same length, and the hypotenuse will always be this length times sin(45o) or times the square root of 0.5.

The length of the hypotenuse, alone, is not sufficient to determine the area of a triangle.

in an isosceles triangle, if the legs have length L, then the hypotenuse has length L square root of 2

When it is an isosceles right angled triangle: with angles that are 90-45-45.

12!!

If the hypotenuse is the square root of three, then the legs are (root 6)/2. If the hypotenuse is 12, then the legs are 6(root 2). This is because, for any given right isosceles triangle, the length of the hypotenuse x is root two times the length of the legs.

Area of the right isosceles triangle: 0.5*16*16 = 128 square units