Area and Perimeter Unit Test

Question

7 of 127 of 12 Items
Question
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

3.2 square inches
3.2 square inches

20 square inches
20 square inches

6.4 square inches

Answer 1

To find the area of the scale drawing, we need to use the scale factor between the actual triangle and the scale drawing.

Scale Factor = Actual Height / Scale Height
Scale Factor = 5 inches / 2 inches
Scale Factor = 2.5

To find the area of the scale drawing, we 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 * (1/2 * 8 * 5)
Area of Scale Drawing = 6.25 * 20
Area of Scale Drawing = 125 square inches

Therefore, the area of Crystal's scale drawing is 6.25 square inches.