Two parts of this square shaded. The other two parts are unshaded. What is the ratio of the shaded area to the unshaded area? Give your answer in its simplest form.
4cm
4cm
8cm
8cm
The total area of the square is 8cm x 8cm = 64cm². The shaded area is 2/4 of the total area, which is 32cm². The unshaded area is 2/4 of the total area, which is also 32cm². Therefore, the ratio of the shaded area to the unshaded area is 32:32, or simply 1:1.
To find the ratio of the shaded area to the unshaded area, we first need to determine the areas of the shaded and unshaded parts.
The square has side lengths of 8 cm, so its total area is 8 cm * 8 cm = 64 cm².
Since two parts of the square are shaded, we need to find the area of the shaded region. Each shaded part forms a right-angled triangle with leg lengths of 4 cm and 8 cm. The area of one shaded triangle can be calculated as (1/2) * 4 cm * 8 cm = 16 cm².
Since there are two shaded triangles, the total area of the shaded region is 2 * 16 cm² = 32 cm².
To find the area of the unshaded region, we subtract the shaded area from the total area of the square: 64 cm² - 32 cm² = 32 cm².
Thus, the ratio of the shaded area to the unshaded area is 32 cm² : 32 cm², which simplifies to 1:1.