Question

composite figures homework
find the area of each figure.
1
2
3.
4.

Explanation:

Step1: Divide figure 1 into a trapezoid and a triangle

Trapezoid area formula: $A_1=\frac{(a + b)h}{2}$, where $a = 9$, $b=12$, $h = 4$. Triangle base $b_1=12$, height $h_1 = 5$.
$A_{trapezoid}=\frac{(9 + 12)\times4}{2}=\frac{21\times4}{2}=42$ $cm^2$

Step2: Calculate triangle area

$A_{triangle}=\frac{1}{2}\times12\times5 = 30$ $cm^2$

Step3: Sum up areas

$A_1=A_{trapezoid}+A_{triangle}=42 + 30=72$ $cm^2$

Step4: For figure 2, consider a large rectangle minus a small rectangle

Large rectangle: length $l=3 + 5+3=11$ ft, width $w = 7$ ft. Small rectangle: length $l_1 = 5$ ft, width $w_1=4.5$ ft.
$A_{large - rectangle}=11\times7 = 77$ $ft^2$

Step5: Calculate small - rectangle area

$A_{small - rectangle}=5\times4.5=22.5$ $ft^2$

Step6: Find the area of figure 2

$A_2=A_{large - rectangle}-A_{small - rectangle}=77-22.5 = 54.5$ $ft^2$

Step7: For figure 3, divide into a triangle, a rectangle and a smaller rectangle

Triangle: base $b_2=15$, height $h_2=9 - 1=8$. Large rectangle: length $l_2 = 15$, width $w_2=7$. Small rectangle: length $l_3=1.5$, width $w_3 = 3$.
$A_{triangle}=\frac{1}{2}\times15\times8=60$ $m^2$
$A_{large - rectangle}=15\times7 = 105$ $m^2$
$A_{small - rectangle}=1.5\times3=4.5$ $m^2$

Step8: Sum up areas of figure 3

$A_3=A_{triangle}+A_{large - rectangle}+A_{small - rectangle}=60+105 + 4.5=169.5$ $m^2$

Step9: For figure 4, divide into a rectangle and two triangles

Rectangle: length $l_4=20 - 4-4=12$, width $w_4=3$. Triangles: base $b_3 = 4$, height $h_3=18 - 12=6$.
$A_{rectangle}=12\times3=36$ $yd^2$
$A_{one - triangle}=\frac{1}{2}\times4\times6 = 12$ $yd^2$
$A_{two - triangles}=2\times12=24$ $yd^2$

Step10: Calculate area of figure 4

$A_4=A_{rectangle}+A_{two - triangles}=36+24=60$ $yd^2$

Answer:

1. $72$ $cm^2$
2. $54.5$ $ft^2$
3. $169.5$ $m^2$
4. $60$ $yd^2$