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 points
Captionless Image
4.5 square inches
18 square inches
6.5 square inches
9 square inches
the image shows a triangle and it is split perfectly in half right from the very top point to the flat bottom and on the right side of the split triangle shows 4in and on the flat bottom of the split triangle shows 9in
To find the area of the scale drawing, we first need to find the base of the triangle in the scale drawing. Since the height of the scale drawing is 2 inches, we can use the height of the original triangle to calculate the scale factor.
Let's say the original height of the triangle is x inches. Since the original height is 6, we have:
6/x = 2/2
=> 6/x = 1
=> x = 6
Now that we have the original base and height, we can calculate the area of the original triangle.
Area of original triangle = (1/2) * base * height
= (1/2) * 6 * 6
= 18 square inches
Since the scale drawing is 1/3 of the actual size, we have:
Area of scale drawing = (1/3)^2 * 18
= (1/9) * 18
= 2 square inches
Therefore, the area of the scale drawing is 2 square inches.
Got it! In that case, we can calculate the area of the scaled triangle shown in the image.
Since the height of the scaled drawing is 2 in, we can calculate the scale factor as follows:
Original height = 6 in
Scale drawing height = 2 in
Scale factor = 2 / 6 = 1 / 3
Next, we calculate the base of the scaled triangle using the base of the original triangle:
Original base = 9 in
Scale drawing base = 1/3 * 9 in = 3 in
Now we can calculate the area of the scaled triangle:
Area = (1/2) * base * height
= (1/2) * 3 * 2
= 3 square inches
Therefore, the area of the scaled drawing of the triangle is 3 square inches.