Question

The diagram shows the floor plan for Harry's new tree house. The entry terrace on the tree house is shaped like an isosceles trapezoid.
The entry terrace has an area of ___ square feet. The total area of the tree house is ___ square feet.

Answer 1

Answer:

1. 48 square feet

2. 308 square feet

Step-by-step explanation:

1.

The entry terrace is shaped as a trapezoid and the area of a trapezoid is given as:

Area of Trapezoid = $\frac{1}{2}(b_1+b_2)h$

Where

b_1 and b_2 are the 2 parallel bases

and h is the perpendicular height

From the diagram, we see that the 2 bases are 16 and 8 and height is 4.

Plugging into the formula, we get:

Area of Entry Terrace = $\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(16+8)*4=\frac{1}{2}(24)(4)=48$

2.

The total area comprises of the area of entry terrace + playroom + back porch.

The area of the back porch is 6 * 6 = 36 (it is shaped like a square and square has area of side * side)

The area of the playroom is 14 * 16 = 224 (it is a rectangle and rectangle has area of base * height)

Total area of treehouse = 48 + 36 + 224 = 308 square feet

Answer 2

Answer:

The entry terrace has an area of

48

square feet. The total area of the tree house including the entrance, porch, and side deck is

350

square feet.

Step-by-step explanation:

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