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Δ


X

Y

Z
and
Δ

A

B

C
are similar triangles. Given the dimensions shown in the diagram, what is the area of
Δ

A

B

C
? Express the answer in square units.

Δ ⁢ X ⁢ Y ⁢ Z and Δ ⁢ A ⁢ B ⁢ C are similar triangles. Given the dimensions shown-example-1
User Ord
by
5.6k points

1 Answer

3 votes

Answer:

3.528

Explanation:

the scale factor from the large triangle to the smaller triangle is 1/2. All of the side lengths of the small triangle is 1/2 the side lengths of the large triangle.

A = 1/2 (bh) The area of a triangle. I need to know the base and the height of the little triangle to figure out the area. If I use AC as the base, the length is given to me. It is 4.2. I do not have the height of the base, but I know that it is half of the height of the large triangle and that number is given to me. It is 3.36, if I divide that by 2, I get 1.68. Now I know all that I need to find the area.

A = 1/2(4.2)(1.68)

3.528Units^2

User Mattwise
by
6.1k points