Question

find the area of each figure. corners that look square are square. dimensions are in centimeters. 26. 20 40 10 50 27. 2 5 28. find the area of the shaded portion of this figure. dimensions are in meters. 8 2 4 16

Explanation:

Step1: Analyze figure 26

Split it into two rectangles. One rectangle has dimensions 20 cm by (50 - 40) cm and the other has dimensions 40 cm by 10 cm.

Step2: Calculate area of first rectangle in figure 26

The area of a rectangle is $A = l\times w$. For the first rectangle with $l = 20$ cm and $w=(50 - 40)=10$ cm, $A_1=20\times10 = 200$ $cm^2$.

Step3: Calculate area of second rectangle in figure 26

For the second rectangle with $l = 40$ cm and $w = 10$ cm, $A_2=40\times10=400$ $cm^2$.

Step4: Total area of figure 26

$A_{26}=A_1 + A_2=200+400 = 600$ $cm^2$.

Step5: Analyze figure 27

It is a combination of a rectangle and a semi - circle. The area of the rectangle is $A_{rect}=l\times w$ with $l = 5$ cm and $w = 4$ cm (diameter of semi - circle is 4 cm, so radius $r = 2$ cm), and the area of a semi - circle is $A_{semicircle}=\frac{1}{2}\pi r^2$.

Step6: Calculate area of rectangle in figure 27

$A_{rect}=5\times4 = 20$ $cm^2$.

Step7: Calculate area of semi - circle in figure 27

$A_{semicircle}=\frac{1}{2}\pi\times2^2=2\pi$ $cm^2$.

Step8: Total area of figure 27

$A_{27}=20 + 2\pi\approx20+2\times3.14=20 + 6.28=26.28$ $cm^2$.

Step9: Analyze figure 28

Find the area of the large triangle and the small triangle. The area of a triangle is $A=\frac{1}{2}bh$. For the large triangle with $b = 16$ m and $h = 8$ m, and for the small triangle with $b = 4$ m and $h = 2$ m.

Step10: Calculate area of large triangle in figure 28

$A_{large}=\frac{1}{2}\times16\times8=64$ $m^2$.

Step11: Calculate area of small triangle in figure 28

$A_{small}=\frac{1}{2}\times4\times2 = 4$ $m^2$.

Step12: Calculate area of shaded region in figure 28

$A_{shaded}=A_{large}-A_{small}=64 - 4=60$ $m^2$.

Answer:

1. $600$ $cm^2$
2. $20 + 2\pi\approx26.28$ $cm^2$
3. $60$ $m^2$