Answer:
90 cm^2
Step-by-step explanation:
The scale factor between triangle ABC and triangle PQR is 4:6 or 2:3
The scale factor is 2/3
When relating areas, we use the scale factor squared
Area of ABC = scale factor squared * Area of PQR
40 = (2/3) ^2 Area of PQR
40 =4/9 Area of PQR
Multiply each side by 9/4
40 *9/4 = 9/4 *4/9 * Area of PQR
90 = Area of PQR
When we work with lengths of similar figures, we multiply by the scale factor.
When we work with areas of similar figures, we have a length and a width, so we are really multiplying by the scale factor two times, or the scale factor squared.
A = l*w
A = SF (l) * SF (w)
= SF ^2 lw
So the area of the new figure is the scale factor squared times the area of the old figure.
A new = SF^2 A old
To get from the old figure to the new figure we multiply by 6/4 or 3/2
A new = (3/2)^2 (40)
A new = 9/4 * 40
= 90
