Area and Perimeter Unit Test
8 of 158 of 15 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
20 square inches
20 square inches
1.6 square inches
1.6 square inches
3.2 square inches
3.2 square inches
6.4 square inches
S.A = 382 cm2
To find the area of the scale drawing, we need to use the scale factor between the actual triangle and the scale drawing.
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 / 2
Scale factor = 2.5
Since area is proportional to the square of the scale factor, we can calculate the area of the scale drawing by squaring the scale factor and multiplying it 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 * base * height)
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 125 square inches.