Use the image to answer the question.
An illustration shows a triangle with a base labeled 8 inches. A line runs through the center of the triangle from the apex to the base. This perpendicular height is labeled 5 inches.
Crystal cuts a piece of wood into the shape of a triangle. The height of the triangle is 5 inches, and the base of the triangle measures 8 inches. Crystal makes a scale drawing of the triangle. If the height of her scale drawing is 2 inches, what is the area of her scale drawing?
(1 point)
Responses
1.6 square inches
1.6 square inches
20 square inches
20 square inches
6.4 square inches
6.4 square inches
3.2 square inches
3.2 square inches
To find the area of the scale drawing, you need to find the scale factor first. The scale factor is the ratio of the height of the actual triangle to the height of the scale drawing.
Scale Factor = Actual Height / Scale Drawing Height
Scale Factor = 5 inches / 2 inches
Scale Factor = 2.5
Now, to find the area of the scale drawing, you need to square the scale factor and multiply by the area of the actual triangle.
Area of Scale Drawing = Scale Factor^2 * Area of Actual Triangle
Area of Scale Drawing = 2.5^2 * (1/2 * 8 * 5)
Area of Scale Drawing = 6.25 * 20
Area of Scale Drawing = 125 / 2
Area of Scale Drawing = 62.5 square inches
Since the scale drawing is 2-dimensional, the area will be in square inches. So, the area of Crystal's scale drawing is 62.5 square inches.