Question 18. The diagram shows a rectangle made from three gray squares, each of an area of 25 cm2, inside a larger white rectangle. Two of the vertices of the gray rectangle touch the midpoints of the shorter sides of the white rectangle, and the other two vertices of the gray rectangle touch the other two sides of the white rectangle. What is the area in cm2 of the white rectangle? If we take a closer look at our white rectangle and gray squares, since we know that the gray squares are touching the white rectangle at vertices, we know that we also have four white triangles, and we also know that the area of one of the gray squares is 25. Let's start off by finding the area of the triangles. We can label the whole white rectangle as height times base, and since we know that the shorter sides, h, are divided equally in half by the gray rectangle, we can call this h halves. So this means the height of each of the triangles will be h halves, and if we lay them out flat, we would have 2 base. So the area of the sum of the four triangles is 1 half times 2b times 1 half of h. If we simplify this, we get 1 half times base times height. So that means the area of the white triangles is half of the area of the entire white rectangle. Knowing that the three gray squares are each 25, we get 25 plus 25 plus 25, or 75. So this means that the gray rectangle is equal to 75, and the white triangles are equal to half of the total area. That would also imply that the gray rectangle is the other half of the area. So when we do 1 half plus 1 half, we will get our full area of the white rectangle. So 75 plus 75 gives us our answer, which is d, 150.

geometry

rectangle

area

squares

problem-solving