Question

select the correct answer from each drop - down menu.
the theater club draws a tree on the set background. the plan for the size of the tree is shown below. what is the approximate area they will have to paint to fill in this tree?
the top of the tree is a triangle. its area is approximately $square$ $\text{ft}^2$.
the second layer of the tree is a trapezoid. its area is approximately $square$ $\text{ft}^2$.
the trunk of the tree is a rectangle. its area is approximately $square$ $\text{ft}^2$.
the total area of the tree is approximately $square$ $\text{ft}^2$.

Explanation:

Step1: Find triangle area

First, assume the triangle's height is 1.5 ft (since total height is 5 ft, split roughly: triangle 1.5 ft, trapezoid 3 ft, rectangle 0.5 ft). Area formula: $\frac{1}{2} \times base \times height$
$\frac{1}{2} \times 3 \times 1.5 = 2.25$ $\text{ft}^2$

Step2: Find trapezoid area

Use trapezoid area formula: $\frac{1}{2} \times (base_1 + base_2) \times height$
$\frac{1}{2} \times (3 + 4) \times 3 = 10.5$ $\text{ft}^2$

Step3: Find rectangle area

Use rectangle area formula: $length \times width$, assume rectangle height is 0.5 ft
$0.2 \times 0.5 = 0.1$ $\text{ft}^2$

Step4: Calculate total area

Sum the three areas: $2.25 + 10.5 + 0.1$
$2.25 + 10.5 + 0.1 = 12.85$ $\text{ft}^2$
(Note: If using a different reasonable height split, values may shift slightly, but this is a standard approximation.)

Answer:

The top of the tree is a triangle. Its area is approximately $\boldsymbol{2.25}$ $\text{ft}^2$.
The second layer of the tree is a trapezoid. Its area is approximately $\boldsymbol{10.5}$ $\text{ft}^2$.
The trunk of the tree is a rectangle. Its area is approximately $\boldsymbol{0.1}$ $\text{ft}^2$.
The total area of the tree is approximately $\boldsymbol{12.85}$ $\text{ft}^2$.