Question

1. calculate the area of the following composite shape: 3k
2. calculate the perimeter of the following composite shape. round your answer to one decimal place. 3k
3. find the surface area and volume of the following shape. round your answer to two decimal places. 6k

height = 21 ft
diameter = 10 ft

Explanation:

1. Calculate the area of the composite shape

Step1: Calculate the area of the rectangle

The formula for the area of a rectangle is \(A_{rectangle}=l\times w\). Here, \(l = 15\space cm\) and \(w=12\space cm\). So, \(A_{rectangle}=15\times12 = 180\space cm^{2}\)

Step2: Calculate the area of the triangle

The formula for the area of a triangle is \(A_{triangle}=\frac{1}{2}\times b\times h\). Here, \(b = 7\space cm\) and \(h = 12\space cm\). So, \(A_{triangle}=\frac{1}{2}\times7\times12=42\space cm^{2}\)

Step3: Calculate the total area

The total area \(A = A_{rectangle}+A_{triangle}\). So, \(A=180 + 42=222\space cm^{2}\)

Step1: Calculate the length of the semic - circle

The formula for the circumference of a full - circle is \(C = \pi d\). For a semicircle, \(C_{semicircle}=\frac{1}{2}\pi d\). Given \(d = 14\space cm\), so \(C_{semicircle}=\frac{1}{2}\times\pi\times14=7\pi\space cm\approx 21.99\space cm\)

Step2: Calculate the sum of the straight sides

We have two sides of length \(20\space cm\) and one side of length \(14\space cm\). The sum of the straight sides \(S=20 + 20+14=54\space cm\)

Step3: Calculate the perimeter

The perimeter \(P=54 + 21.99=75.99\approx76.0\space cm\)

Step1: Find the radius

Given \(d = 10\space ft\), so \(r=\frac{d}{2}=5\space ft\)

Step2: Calculate the lateral surface area

The formula for the lateral surface area of a cylinder is \(A_{lateral}=2\pi r h\). Here, \(r = 5\space ft\) and \(h = 21\space ft\). So, \(A_{lateral}=2\times\pi\times5\times21=210\pi\space ft^{2}\approx 659.73\space ft^{2}\)

Step3: Calculate the area of the two bases

The formula for the area of a circle is \(A_{base}=\pi r^{2}\). For two bases, \(A_{bases}=2\pi r^{2}\). So, \(A_{bases}=2\times\pi\times5^{2}=50\pi\space ft^{2}\approx157.08\space ft^{2}\)

Step4: Calculate the total surface area

\(A_{total}=A_{lateral}+A_{bases}\). So, \(A_{total}=659.73+157.08 = 816.81\space ft^{2}\)

Volume

Answer:

\(222\space cm^{2}\)

2. Calculate the perimeter of the composite shape