26. find the perimeter of this figure. cor - ners that look square are square. dimensions are in centimeters. 27. find the area of this scalene triangle. dimensions are in meters. 28. find the area of the shaded portion of this rectangle. dimensions are in kilo - meters. 29. wx is 5 1/2 inches. xy is 12 3/10 inches. yz is 3 2/5 inches. find wz. 30. a base of the right solid has an area of 45 ft². the height of the right solid is 10 ft. find the volume of the right solid.

Question

Accepted Answer

### 26.
# Explanation:
## Step1: Calculate the circumference of the circle
The two semi - circles at the ends form a complete circle. The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 4$ cm, $C=2\pi\times4 = 8\pi$ cm.
## Step2: Calculate the length of the straight parts
The length of the two straight parts is $2\times10=20$ cm.
## Step3: Calculate the perimeter
The perimeter $P$ of the figure is the sum of the circumference of the circle and the lengths of the straight parts. So $P = 8\pi+20$. Using $\pi\approx3.14$, $P\approx8\times3.14 + 20=25.12+20 = 45.12$ cm.

# Answer:
$45.12$ cm

### 27.
# Explanation:
## Step1: Use the formula for the area of a triangle
The formula for the area of a triangle is $A=\frac{1}{2}\times base\times height$. Here, the base $b = 8$ m and the height $h = 15$ m.
## Step2: Calculate the area
Substitute the values into the formula: $A=\frac{1}{2}\times8\times15$. First, $8\times15 = 120$, then $\frac{1}{2}\times120=60$ $m^{2}$.

# Answer:
$60$ $m^{2}$

### 28.
# Explanation:
## Step1: Calculate the area of the rectangle
The formula for the area of a rectangle is $A_{r}=length\times width$. Here, $length = 10$ km and $width = 8$ km, so $A_{r}=10\times8 = 80$ $km^{2}$.
## Step2: Calculate the area of the triangle
The formula for the area of a triangle is $A_{t}=\frac{1}{2}\times base\times height$. Here, $base = 8$ km and $height = 5$ km. So $A_{t}=\frac{1}{2}\times8\times5=20$ $km^{2}$.
## Step3: Calculate the area of the shaded region
The area of the shaded region $A = A_{r}-A_{t}$. So $A=80 - 20=60$ $km^{2}$.

# Answer:
$60$ $km^{2}$

### 29.
# Explanation:
## Step1: Convert the mixed numbers to improper fractions
$WX = 5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2}$, $XY=12\frac{3}{10}=\frac{12\times10+3}{10}=\frac{123}{10}$, $YZ = 3\frac{2}{5}=\frac{3\times5+2}{5}=\frac{17}{5}$.
## Step2: Find a common denominator
The common denominator of $2$, $10$ and $5$ is $10$. $\frac{11}{2}=\frac{11\times5}{2\times5}=\frac{55}{10}$, $\frac{17}{5}=\frac{17\times2}{5\times2}=\frac{34}{10}$.
## Step3: Add the fractions
$WZ=WX + XY+YZ=\frac{55}{10}+\frac{123}{10}+\frac{34}{10}=\frac{55 + 123+34}{10}=\frac{212}{10}=21.2$ inches.

# Answer:
$21.2$ inches

### 30.
# Explanation:
## Step1: Use the formula for the volume of a right - solid
The formula for the volume of a right - solid (prism) is $V=A\times h$, where $A$ is the area of the base and $h$ is the height.
## Step2: Substitute the values
Given $A = 45$ $ft^{2}$ and $h = 10$ ft. Then $V=45\times10=450$ $ft^{3}$.

# Answer:
$450$ $ft^{3}$

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QUESTION IMAGE

Question

Explanation:

26.

Step1: Calculate the circumference of the circle

Step2: Calculate the length of the straight parts

Step3: Calculate the perimeter

Step1: Use the formula for the area of a triangle

Step2: Calculate the area

Step1: Calculate the area of the rectangle

Step2: Calculate the area of the triangle

Step3: Calculate the area of the shaded region

Answer:

27.