To find the area of the scale drawing, we need to first find the base of the triangle in the scale drawing. The height has been given as 2in, so we need to determine the scale factor in order to find the base.
Let's say the actual height of the triangle is h and the actual base is b. The scale factor is the ratio of the height of the scale drawing to the actual height:
Scale factor = Height of scale drawing / Actual height = 2in / h
Now, we need to find the base in the scale drawing using the scale factor:
Base in scale drawing = Scale factor * Actual base
Base in scale drawing = (2in / h) * b
Now, we know that the area of a triangle is given by:
Area = 0.5 * base * height
Plugging in the values for the scale drawing:
Area of scale drawing = 0.5 * (2in/h * b) * 2in
Area of scale drawing = (2in^2 / h) * b
Since the scale drawing is similar to the actual triangle, the ratio of areas will be the square of the ratio of sides:
Area of scale drawing / Actual area = (2in / h)^2
We can see that (2in / h)^2 is the ratio of the heights squared since the height is squared in the formula for area of a triangle.
So, Area of scale drawing = (2in/h)^2 * Actual area
Area of scale drawing = (2in / h)^2 * 36 sq inches
Area of scale drawing = (2in / h)^2 * 36 sq inches
Given the actual height is 6in, we can find the area of the scale drawing:
Area of scale drawing = (2in / 6in)^2 * 36 sq inches
Area of scale drawing = (1/3)^2 * 36 sq inches
Area of scale drawing = (1/9) * 36 sq inches
Area of scale drawing = 4 sq inches
Therefore, the area of the scale drawing is 4 square inches.
A scale drawing of the triangle below is made. The height of the scale drawing is 2in. What is the area of the scale drawing?
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2 pontos
Imagem sem legenda
4.5 square inches
18 square inches
6.5 square inches
9 square inches
1 answer