Isosceles right triangles are a special right triangle because it follows the 45-45-90 rule. If one leg was x, then the other leg was also x and the hypotenuse was x√2.
Using that information, we can confirm that the legs of the triangle are 2 since 6√2 divided by √2 is 6.
Now that we have the legs of the triangle, we can use the formula for the area of the triangle to solve: (remember that area = (bh)/2)
[tex] A=\frac{6*6}{2} [/tex]
Firstly, multiply the numerator: [tex] A=\frac{36}{2} [/tex]
Next, divide, and your answer will be A = 18. Since the square and the right triangle have the same area, your answer is 18, or h.
An isosceles right triangle is a 45°-45°-90° triangle. 45°-45°-90° triangles' hypotenuses are always equal to their leg length times the square root of two.
For 45°-45°-90° triangles:
Leg = x
Hypotenuse = x√(2)
The length of the hypotenuse is given (6√(2)), so we can easily find the length of its legs. If we divide the hypotenuse by √(2), we are left with 6. This is the leg length.
To find the area of the triangle (and thus the area of the square), use the formula for area of a triangle, A = bh/2. Our b, base, is 6, and our h, height, is also 6. Plug these values in accordingly and solve.
A = 6 * 6/2
A = 36/2
A = 18
The area of the triangle (and that of the square) is 18 units squared.
Answer:
The area of the square is 18 units².
h) 18
