Question

problems 7 - 8: tamiya created a scaled copy of triangle a with an area of 72 square units.

1. how many times greater is the area of the scaled copy compared to the area of triangle a?
2. what scale factor did tamiya apply to triangle a to create the scaled copy?

Explanation:

Step1: Calculate area of triangle A

From the grid, base $b = 3$ units and height $h=3$ units. Using the formula $A=\frac{1}{2}bh$, we have $A_{A}=\frac{1}{2}\times3\times3=\frac{9}{2} = 4.5$ square - units.

Step2: Find ratio of areas for question 7

The area of the scaled - copy is $A_{scaled}=72$ square units. The ratio of the area of the scaled copy to the area of triangle A is $\frac{A_{scaled}}{A_{A}}=\frac{72}{4.5}=16$.

Step3: Find scale factor for question 8

If the scale factor is $k$, the ratio of the areas of two similar figures is $k^{2}$. Since $\frac{A_{scaled}}{A_{A}} = k^{2}=16$, then $k = 4$.

Answer:

1. 16
2. 4