Question

Six right triangles are shown. Each side of each triangle is also the side of a square.

Answer 1

The area of the small triangle in six right triangles are shown is 1/25 units² and the area of the small square is 1 units².

What is the area of square?

Area of square is the square of its sides length. It can be given as,

A=a^2

Here, (a) is the length of the side of the square

The legs of the smallest triangle is 1-1 units long. Thus, the area of this triangle is,

$A=\dfrac{1\times1}{2}\\A=\dfrac{1}{2}\rm\; unit^2$

The area of small squares with side 1 is,

$A=1^2\\A=1 \rm \;unit^2$

Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of other two legs of the right angle triangle.

The hypotenuse side length of this triangle is,

$h=\sqrt{1^2+1^2}\\h=\sqrt{2}$

Thus, the area of the square with √2 side is,

$A=\sqrt{2}^2\\A=2\rm\; unit^2$

Similarly, the area of all the squares and triangle with the different sides can be found out.

Thus, the area of the small triangle in six right triangles are shown is 1/25 units² and the area of the small square is 1 units².

Learn more about the area of square here;

https://brainly.com/question/1658516

#SPJ1