The figure below is not drawn to scale. The ratio of the triangle ABC to the area of triangle DEC to the area of the triangle FGH is 7:5:3. If 20% of the area of triangle DEC is shaded, what percentage of the figure is unshaded?
The answer is not 80%. It asks you what the percentage of the figure is unshaded. The percentage of the figure, not just triangle DEC.
To determine the percentage of the figure that is unshaded, we need to find the ratio of the unshaded area to the total area of the figure.
1. Let's assign variables to the areas of the triangles:
- Area of triangle ABC = 7x
- Area of triangle DEC = 5x
- Area of triangle FGH = 3x
2. The shaded area represents 20% of the area of triangle DEC, so the shaded area is 0.2 * 5x = x.
3. To find the unshaded area, we subtract the shaded area from the total area of triangle DEC: 5x - x = 4x.
4. The total area of the figure is the sum of the areas of triangles ABC, DEC, and FGH: 7x + 5x + 3x = 15x.
5. The unshaded area is equal to 4x, so the percentage of the figure that is unshaded is (4x / 15x) * 100% = 26.67%.
Therefore, 26.67% of the figure is unshaded.
To find the percentage of the figure that is unshaded, we first need to determine the areas of triangles ABC, DEC, and FGH.
Given that the ratio of triangle ABC to triangle DEC to triangle FGH is 7:5:3, let's assign a value to the area of triangle ABC.
Let's assume the area of triangle ABC is 7 units.
Therefore, the area of triangle DEC would be 5 units (since it is in the ratio 7:5:3).
Now, if we know that 20% of triangle DEC is shaded, we can calculate the shaded area.
Shaded area = 20% of 5 units = 0.2 * 5 = 1 unit.
To find the unshaded area of triangle DEC, we subtract the shaded area from the total area:
Unshaded area of triangle DEC = 5 units - 1 unit = 4 units.
Now, if we add up the areas of all three triangles, we get:
Total area = area of triangle ABC + area of triangle DEC + area of triangle FGH
Total area = 7 units + 5 units + 3 units = 15 units.
To find the percentage of the figure that is unshaded, we divide the unshaded area (4 units) by the total area (15 units) and multiply by 100:
Percentage of the figure unshaded = (4 units / 15 units) * 100% ≈ 26.67%.
Therefore, approximately 26.67% of the figure is unshaded.