What is the surface area of the composite figure?

9514 1404 393

  382 cm²

Step-by-step explanation:

The side facing is a trapezoid with bases 8 and 14 cm, and height 7 cm. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(8 +14)(7) = 77 . . . . cm²

The perimeter of the face is ...

  7 cm + 8 cm + 9 cm + 14 cm = 38 cm

The total surface area is the sum of the lateral area and the base area.

  SA = LA + BA

  SA = (38 cm)(6 cm) + 2×(77 cm²) = 228 cm² + 154 cm²

  SA = 382 cm²

The surface area of the composite figure is 382 square centimeters.

Additional comment

The lateral area is the width of a rectangular face (6 cm) times the total of all of the lengths of those faces. That total is the perimeter of the trapezoidal base (38 cm).

There are two trapezoidal bases that contribute area. The first calculation figured the area of one of them.

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.

"exterior angles = 360 / number of sides.

60 = 360 / sides

sides = 360 / 60

sides = 6"