Question

1 label the dimensions in the diagram at the right.
2 find the area of the square in the diagram.
$\boldsymbol{36}$ $in^{2}$
3 find the area of one of the triangles in the diagram.
$\boldsymbol{square}$ $in^{2}$
4 write and solve an equation to find the area of the trapezoid.
show your work.
solution: $\boldsymbol{square}$ $in^{2}$
hint: youll need to add the area of both triangles and the
6 in.
6 in.
6

Explanation:

Step1: Label bottom triangle bases

Assume the two triangles are congruent, so each bottom unlabeled segment is 3 in. (since the total bottom base would be $6 + 3 + 3 = 12$ in., a common trapezoid setup here).

Step2: Calculate area of one triangle

Use triangle area formula $\frac{1}{2} \times base \times height$.
$\frac{1}{2} \times 3 \times 6 = 9$

Step3: Calculate total area of two triangles

Multiply single triangle area by 2.
$9 \times 2 = 18$

Step4: Find trapezoid total area

Add square area and two triangles' area.
$36 + 18 = 54$

Answer:

1. Label the two unlabeled bottom segments as 3 in. each.
2. $36$ in$^2$
3. $9$ in$^2$
4. Equation: $\text{Area of trapezoid} = \text{Area of square} + 2 \times \text{Area of one triangle}$

$\text{Area of trapezoid} = 36 + 2 \times 9 = 54$
Solution: $54$ in$^2$