Question

click the arrows to choose an answer from each menu. the figure can be decomposed into choose... rectangles, or the figure can be decomposed into 4 trapezoids with heights of choose... in. and bases of choose... in. and 5 in. using either method, the total area of the shaded figure is choose... square inches.

Explanation:

Step1: Decomposition into rectangles

The figure can be decomposed into 2 rectangles. One rectangle has dimensions 2 in by 2 in and the other has dimensions 2 in by 3 in (since 5 - 2=3).

Step2: Calculate area of first rectangle

The area of a rectangle is $A = l\times w$. For the first rectangle with $l = 2$ in and $w = 2$ in, $A_1=2\times2 = 4$ square - inches.

Step3: Calculate area of second rectangle

For the second rectangle with $l = 2$ in and $w = 3$ in, $A_2=2\times3 = 6$ square - inches.

Step4: Calculate total area

The total area $A = A_1+A_2=4 + 6=10$ square - inches.

If decomposing into 4 trapezoids:

Step1: Determine trapezoid height

The height of each trapezoid is 0.5 in (since dividing the 2 - inch height into 4 equal parts: $2\div4 = 0.5$ in).

Step2: Determine trapezoid bases

The bases are 2 in and 5 in.

Step3: Calculate area of one trapezoid

The area of a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1 = 2$ in, $b_2 = 5$ in and $h = 0.5$ in. So $A_{trap}=\frac{(2 + 5)\times0.5}{2}=\frac{7\times0.5}{2}=1.75$ square - inches.

Step4: Calculate total area

The total area of 4 trapezoids is $4\times A_{trap}=4\times1.75 = 10$ square - inches.

Answer:

The figure can be decomposed into 2 rectangles, or the figure can be decomposed into 4 trapezoids with heights of 0.5 in and bases of 2 in and 5 in. Using either method, the total area of the shaded figure is 10 square inches.