Q: How do you fine the area of an isosceles right triangle with only the hypotenuse?

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

The hypotenuse only is not sufficient to determine the area of a right triangle, unless the triangle is stated to be isosceles, or there is some other information that allows determination of the length of a side in addition to the hypotenuse. The area of a right triangle with a given hypotenuse only approaches zero as one of the two acute angles approaches zero degrees.

A right triangle with a hypotenuse of 10m and a base of 5m has an area of: 21.65m2

A right triangle with a hypotenuse of length 15 and a leg of length 8 has an area of: 50.75 units2

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.

Related questions

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

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

The hypotenuse only is not sufficient to determine the area of a right triangle, unless the triangle is stated to be isosceles, or there is some other information that allows determination of the length of a side in addition to the hypotenuse. The area of a right triangle with a given hypotenuse only approaches zero as one of the two acute angles approaches zero degrees.

A right triangle with a hypotenuse of 10m and a base of 5m has an area of: 21.65m2

A right triangle with a hypotenuse of length 15 and a leg of length 8 has an area of: 50.75 units2

What is the length of a leg of an isosceles right triangle if it is area is 72 square inches?

No.Additional Information:-Yes providing it's not an isosceles right angle triangle the possible dimensions are:- hypotenuse 8 cm, height 6.4 cm and base 4.8 cm because they comply with Pythagoras' theorem.So the area is:- 1/2*6.4*4.8 = 15.36 square cmNote that if it was an isosceles triangle then the dimensions and area could also be worked out that is why you should have specified in your question the type of triangle.

An isosceles right triangle is a 90 degree triangle that the two non-hypotenuse sides are equal. http://mathworld.wolfram.com/IsoscelesRightTriangle.html Area of a triangle is 1/2 x b x h Area of an isosceles right triangle is 1/2 b2 144 cm2 = 1/2 b2 2 (144 cm2) = 2(1/2 b2) 288 cm2 =b2 16.97 cm = b So the base and height each equal 16.97 cm The hypotenuse can be solved by the Pythagorean Theorem a2 + b2 = c2 288 + 288 = c2 576 = c2 (576).5 = (c2).5 24 = c So the sides of an isosceles right triangle with the area of 144 cm2 are 16.97 cm, 16.97 cm, and 24 cm.

A right triangle has a hypotenuse of length 10 and a leg of length 7 has an area of: 24.99 units2

I do believe you mean RIGHT triangle when you said perpendicular triangle. A right triangle has two legs and a hypotenuse. The area of a right triangle is 1/2 * (first leg) * (second leg) How do you determine which ones are the legs and which one is the hypotenuse? The hypotenuse is ALWAYS the largest number. So, choose the 2 smallest numbers.

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.

I believe you need 2 pieces of data (either an angle or another length) before you can calculate anything about the triangle. Anyone else can correct me if I'm wrong.