The figure below is not drawn to scale. The ratio of the area of triangle ABC to the area of triangle DEC to the area of triangle FGH is 7 : 5 :3. If 20% of the area of triangle DEC is shaded, what percentage of the figure is unshaded? PLEASE SHOW ALL YOUR WORK!!!!!

plz help me

To determine the percentage of the figure that is unshaded, we need to find the ratio of the shaded area to the total area of the figure.

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

Given that 20% of the area of triangle DEC is shaded, we can find the shaded area as follows:
Shaded area = 20/100 * Area of triangle DEC
Shaded area = 20/100 * 5x
Shaded area = x (since 20/100 reduces to 1/5)

Now, to find the total area of the figure, we need to sum up the areas of all the triangles:
Total area = Area of triangle ABC + Area of triangle DEC + Area of triangle FGH
Total area = 7x + 5x + 3x
Total area = 15x

The percentage of the figure that is unshaded can be calculated using the ratio of the shaded area to the total area:
Unshaded area = (Total area - Shaded area) / Total area
Unshaded area = (15x - x) / 15x
Unshaded area = 14x / 15x
Unshaded area = 14/15

To express this as a percentage, we multiply by 100:
Unshaded percentage = (14/15) * 100
Unshaded percentage ≈ 93.33%

Therefore, approximately 93.33% of the figure is unshaded.

To find the percentage of the figure that is unshaded, we need to determine the area of the shaded region first.

Let's start by looking at the ratios given: 7 : 5 : 3. To simplify the calculations, let's assign a variable to the area of triangle DEC. Let's say the area of triangle DEC is A.

According to the ratio, the area of triangle ABC is 7A, and the area of triangle FGH is 3A.

Since 20% of triangle DEC is shaded, the shaded area is 0.2A.

To find the unshaded area, we need to subtract the shaded area from the total area of the figure, which is the combined area of triangles ABC, DEC, and FGH.

The total area of the figure is given by:
Area of triangle ABC + Area of triangle DEC + Area of triangle FGH

= 7A + A + 3A
= 11A

Therefore, the unshaded area is:
Total area of the figure - Shaded area
= 11A - 0.2A
= 10.8A

To find the percentage of the figure that is unshaded, we need to divide the unshaded area by the total area of the figure and then multiply by 100.

Percentage of the figure that is unshaded = (Unshaded area / Total area of the figure) * 100
= (10.8A / 11A) * 100
= 98.18%

So, approximately 98.18% of the figure is unshaded.

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