Question 21. Two congruent isosceles right triangles each have a square inscribed as shown in the diagram. The square marked P has an area of 45. What is the area of the square marked R? Let's take a closer look at these triangles. Let's look at the triangle with the square marked P. If we draw a diagonal line through the square, we notice that the whole triangle is broken up into four equal pieces. With that knowledge, we know that two of the four pieces make up square P. So that means half of the triangle's area is the square, or 45. So, to get the area of the whole triangle, we multiply by two, and get 90. Next, we look at the triangle with the square marked R. And we can also break this up into smaller triangles. Here, we break it up into nine equal triangles. To get the area of each of these small triangles, we take 90, divide it by 9, and get 10. And, we notice that the square marked R is made up of four of these triangles. So we will multiply by four. This will give us our answer, which will be B, 40.

isosceles right triangles

inscribed square

triangle area

geometry problem

area calculation