Answer:
612.5 cm²
Step-by-step explanation:
The ratio of areas of similar figures is the square of the scale factor. The scale factor is the ratio of corresponding side lengths. Here, we must find the scale factor.
__
missing side of A
The only given side of trapezium B corresponds to an unknown side of trapezium A. We can find the length of that unknown side using the area formula.
A = 1/2(b1 +b2)h . . . . . parallel sides b1, b2; height h
98 cm² = 1/2(16 cm +b2)(7 cm) . . . . use known values
28 cm = 16 cm +b2 . . . . . . . . . . divide by 3.5 cm
b2 = 12 cm . . . . . . . . . . . . . . subtract 16 cm
The top side of trapezium A is 12 cm long.
scale factor
Now we have the lengths of corresponding (top) sides, so we can find the scale factor. It is their ratio. We choose to express it as (size of B)/(size of A).,
k = (30 cm)/(12 cm) = 2.5
area of B
The area of trapezium B will be that of trapezium A multiplied by the square of the scale factor:
area B = (k²)(area A) = (2.5²)(area A)
area B = 6.25×98 cm² = 612.5 cm²
The area of trapezium B is 612.5 cm².
