Question

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

Answer 1

Answer:

a. $A_{trapezoid}=228ft^2$

b. $A_{trapezoid}=228ft^2$

c. They are equivalent

Step-by-step explanation:

a. The trapezoid can be divided into two triangles and one rectangle.  For the three figures, the height is 12ft. For the rectangle, the dimensions are 12ftx10ft. Since the legs are of the same length the triangles have a base of 9ft (because the rectangle takes 10 feet from the base of 28 feet and there are 18 feet left over, these 18 are divided equally between the two triangles).

$A_{rectangle}=bh=(10)(12)=120ft^2$

$A_{triangle}=\frac{bh}{2}=\frac{9(12)}{2}=\frac{108}{2}=54ft^2$

$A_{trapezoid}=A_{rectangle}+A_{triangle}+A_{triangle}\\Area=120+54+54=228ft^2$

b. The formula is

$A=h(\frac{B+b}{2})=12(\frac{10+28}{2})=12(19)=228ft^2$

c. They are equivalent