You are going camping with your family for a family reunion. You need to know how many sleeping bags will fit inside the tent you will be using. The floor of the tent is a trapezoid with bases of 10 ft. and 28 ft. The distance between the bases is 12 ft. and the legs of the trapezoidal floor are 15 ft. For the camping trip you will all be using sleeping bags that are 6.7 ft. by 2.3 ft.

a. Calculate the area of the floor of the tent using area formulas for rectangles and triangles.

b. Calculate the area of the floor using the formula for a trapezoid.

c. What did you discover about the two methods of calculating the area of the floor?

d. Find the perimeter of the tent and the perimeter of a sleeping bag.

e. How much area do you need for one sleeping bag?

f. Based on total area alone (ignore odd angles), how many people will be able to sleep in this tent? Explain.

These are 6 questions (from a to f). Each has its complete answer.

a. Calculate the area of the floor of the tent using area formulas for rectangles and triangles.

1) The trapezoid is composed of two congruent triangles and one rectangle.

2) The area of each triangle is: (1/2) bh

3) The base of each triangle is half the difference of the two bases: (28 - 10) / 2 ft

4) The height of each triangle is the separation between the two bases: 12 ft

5) The area of the rectangle is base * height = base * separation between the bases.

6) Calculation of the area of the floor of the tent: two congruent triangles + rectangle

2 * (1/2) * (28 - 10) / 2 * 12 + 10 * 12 = 228 ft²

b. Calculate the area of the floor using the formula for a trapezoid.

formula: area of trapezoid = distance between the bases ₓ (base₁ + base₂) / 2

12 * (28 + 10) / 2 = 228 ft²

c. What did you discover about the two methods of calculating the area of the floor?

The two methods are equivalent, as they are just two ways of calculating the areas by spliting the figure in different ways.

d. Find the perimeter of the tent and the perimeter of a sleeping bag.

The perimeter is the length of all the sides.

Perimeter of the tent: 10ft + 15ft + 28ft + 15ft = 68 ft

Perimeter of each sleeping bag: 6.7 ft + 2.3 ft = 9 ft

e. How much area do you need for one sleeping bag?

area = 6.7 ft * 2.3 ft = 15.41 ft²

f. Based on total area alone (ignore odd angles), how many people will be able to sleep in this tent? Explain.

You have to divide the area of the floor by the area of one sleeping bag to calculate how many sleeping bags fit in the floor:

⇒ 228 ft² / 15.41 ft² = 14.8

Therefore, 14 people can sleep in the tent.