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Area of DEF = 6 sq ft

Find the area of ABC. Please help I need BOTH green and grey boxes please .

Area of DEF = 6 sq ft Find the area of ABC. Please help I need BOTH green and grey-example-1

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Answer:

54 ft^2

(54 in green box; 2 in grey box)

Explanation:

We have 2 similar triangles, ABC and DEF.

The area of triangle DEF is given as 6 sq ft.

Side BC of triangle ABC measures 12 ft.

The corresponding side to BC in triangle DEF is EF. It measures 4 ft.

That gives us a scale factor from triangle DEF to triangle ABC.

To find the scale factor between two similar polygons, divide the length of a side of the second polygon by the length of the corresponding side of the first polygon.

scale factor = BC/EF = (12 ft)/(4 ft) = 3

The scale factor of side lengths is 3.

The ratio of the areas is the square of the scale factor.

ratio of areas = 3^2 = 9

Now multiply the area of the first triangle (DEF) by the ratio of areas to get the area of the second triangle (ABC).

area of triangle ABC = 9 * (area of triangle DEF)

area of triangle ABC = 9 * (6 sq ft)

area of triangle ABC = 54 sq ft

Answer: 54 ft^2

(54 in green box; 2 in grey box)

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