# Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm.

Correct result:

S =  6096.4 cm2

#### Solution:

$p = 2a+b \ \\ \sin \gamma/2 = \dfrac{b/2}{ a } \ \\ b = 2a \sin \gamma/2 = 2a \sin 45^\circ \ \\ p = 2a + b = 2a + 2a \sin 45^\circ = 2a(1+\sin 45^\circ ) \ \\ \ \\ a = \dfrac{ p }{ 2 \cdot (1+\sin 45^\circ ) } = 110.421 \ \\ \ \\ S = \dfrac{1}{2} a^2 = \dfrac{1}{2} 110.421^2 = 6096.4 \ \text{cm}^2 \ \\$

Try calculation via our triangle calculator.

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• ISO Triangle V2
Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
• Isosceles III
The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
• Isosceles trapezoid
The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
• RT 11
Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
• Circle inscribed
Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
• SAS triangle
The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
• Rectangular trapezoid
Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
• Height
Calculate height of the equilateral triangle if its perimeter is 8?
The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart?
• Oil rig
Oil drilling rig is 23 meters height and fix the ropes which ends are 7 meters away from the foot of the tower. How long are these ropes?
• Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6