Question

8. (192) Calculate the area of the shaded square region
inside the larger square please.

Answer 1

90 units squared

Explanation:

To start, we should find the area of the right triangles inside the larger square. We can do so with using the area formula for triangles, which is 1/2bh.

Area of one triangle:

• 1/2bh
• 1/2(3)(9)
• 13.5 units squared

Now that we have the area of one triangle, we can determine the area of the non-shaded region, which will help later.

Area of non-shaded region:

• 4(13.5) -- because there are 4 triangles, we multiply the area of one triangle by 4
• 54 units squared

Our last step is as follows. We subtract the area of the non-shaded region from the area of the large square. Finding the area of a square is as simple as bh. However, it may appear that we don't have the measurements to determine the area. To figure this out, let's go back to the properties of a square. A square is defined most simply as a quadrilateral (4 sided figure) with congruent (equal) sides. using this information, we can conclude that if we know one side, we know the measurement of all the sides. The left side of the larger square gives us what we need to determine the measurements of all the sides of the square. 9 units and 3 units make up one side of the square, therefore one side of the square is 12. Now that we have the side measurements for the square, we can determine the area of the large square.

Area of large square:

• bh
• (12)(12)
• 144 units squared

Great! Now we subtract the area of the four triangles from the larger square, leaving us with the shaded region.

Area of the shaded region:

• 144 - 54
• 90 units squared

There you have it. The area of the shaded region is 90 units squared. I hope this helped!