Question

A composite figure is shown. 10 ft А 6 ft - 10 ft तो 12 ft B C 12 ft 4 ft Determine whether each statement about the composite figure is correct. Choose True or False for each statement. a. The area of region B is the same as the area of region C. True False b. The area of region A is double the area of region C. True False C. The area of the composite figure is 180 square feet. True False True False d. The sum of the areas of regions B and C is less than the area of region A.

Answer 1

ANSWERS

a. True

b. False

c. True

d. False

Step-by-step explanation

a. Regions B and C are both rectangles with the same side lengths. Therefore, they are congruent rectangles, so the areas must be the same.

b. For this item we have to find the areas of region A and C.

Region A is a trapezoid. The area is:

`A_A=((10+18))/(2)*6=84ft^2`

The area of region C is:

`A_C=12ft*4ft=48ft^2`

Two times the area of region C is 96ft², so this statement is false.

c. In the previous item we found the area of regions A and C. From item a we know that the area of region C is the same area of region B. The area of the figure is:

`A=A_A+A_B+A_C=84+48+48=180ft^2`

This statement is true.

d. Since regions B and C have the same area, saying 'the sum of the areas of regions B and C' is the same as saying 'double the area of region C'. From item b, we know that the sum of areas B and C is 96ft², and area A is 84ft².

Area A is less than the sum of areas B and C. Therefore this statement is false.