Question

figure k is a scale image of figure t, as shown. the scale that maps figure k onto figure t is 1 : 3½. what is the area of figure t? figure k has a vertical side labeled 4 and a horizontal side labeled 3; figure t is a larger triangle.

Explanation:

Step1: Calculate area of Figure K

Figure K is a right triangle with legs 3 and 4. The area formula for a triangle is $A = \frac{1}{2} \times base \times height$. So, $A_K = \frac{1}{2} \times 3 \times 4 = 6$.

Step2: Determine the scale factor for area

The scale factor for linear dimensions is $k = 3\frac{1}{2}=\frac{7}{2}$. For area, the scale factor is $k^2$. So, $k^2 = (\frac{7}{2})^2=\frac{49}{4}$.

Step3: Calculate area of Figure T

The area of Figure T is the area of Figure K multiplied by the area scale factor. So, $A_T = A_K \times k^2 = 6 \times \frac{49}{4}=\frac{294}{4} = 73.5$.

Answer:

73.5