Question

name
date:
area & volume
color by number activity
solve the math problems (and solve each math problem provided on the worksheet. use your answer to fill in the spaces. match answers to letter each answer corresponds to a specific letter in the answer key. write your answer and write the question number and color in the appropriate boxes in the design table. each number in the design table is associated with a specific color. use the color indicated for each number to color the corresponding part of the design. make sure you have matched the letters, questions and colors correctly)

1. find the area of the trapezoid
2. find the area of the triangle. round to the nearest tenth.
3. find the area of the rectangle
4. find the area of the parallelogram

the area of a triangle is 128 square centimeters, and height is 8 centimeters. what is the base of the triangle?
find the area of the square
find the area of the parallelogram. round to the nearest tenth.

Explanation:

Step1: Recall trapezoid area formula

The formula for the area of a trapezoid is $A=\frac{(a + b)h}{2}$, where $a$ and $b$ are the lengths of the parallel - sides and $h$ is the height. For the trapezoid with $a = 12$ cm, $b = 20$ cm and $h=14$ cm, we substitute these values into the formula.

Step2: Calculate the sum of parallel sides

$a + b=12 + 20=32$ cm.

Step3: Calculate the area

$A=\frac{(12 + 20)\times14}{2}=\frac{32\times14}{2}=32\times7 = 224$ $cm^{2}$.

Step4: Recall triangle area formula

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height. For the triangle with $b = 7$ cm and $h = 3.5$ cm, we substitute these values.

Step5: Calculate the triangle area

$A=\frac{1}{2}\times7\times3.5=12.25\approx12.3$ $cm^{2}$ (rounded to the nearest tenth).

Step6: Recall rectangle area formula

The formula for the area of a rectangle is $A = lw$, where $l$ is the length and $w$ is the width. For the rectangle with $l = 13$ cm and $w = 7.3$ cm, we have $A=13\times7.3 = 94.9$ $cm^{2}$.

Step7: Recall parallelogram area formula

The formula for the area of a parallelogram is $A = bh$, where $b$ is the base and $h$ is the height. For the parallelogram with $b = 15$ in and $h = 9$ in, $A=15\times9=135$ $in^{2}$.

Step8: Find the base of a triangle

Given $A = 128$ $cm^{2}$ and $h = 8$ cm, from the formula $A=\frac{1}{2}bh$, we can solve for $b$. First, rewrite the formula as $b=\frac{2A}{h}$. Then substitute $A = 128$ and $h = 8$: $b=\frac{2\times128}{8}=32$ cm.

Step9: Recall square area formula

If the diameter of the inscribed circle is $3$ cm, then the side - length of the square is also $3$ cm. The formula for the area of a square is $A = s^{2}$, so $A=3^{2}=9$ $cm^{2}$.

Step10: Calculate another parallelogram area

For the parallelogram with $b = 8.25$ in and $h = 5.4$ in, using the formula $A = bh$, we get $A=8.25\times5.4 = 44.55\approx44.6$ $in^{2}$ (rounded to the nearest tenth).

Answer:

1. $224$ $cm^{2}$
2. $12.3$ $cm^{2}$
3. $94.9$ $cm^{2}$
4. $135$ $in^{2}$
5. $32$ cm
6. $9$ $cm^{2}$
7. $44.6$ $in^{2}$