Question

1. calculating the area of the following 2 - d shapes: a. circle with radius 44 mm b. triangle with base 18 m, height 9 m, side 13 m c. rectangle with length 85 m, width 52 m d. composite 2 - d shape with height 96 m, base 75 m 2. name the following prisms: a. triangular - based prism b. octagonal - based prism c. rectangular - based prism d. another prism palah says that diagram a is the net of a right octagonal prism. manon disagrees. she says that diagram b is the

Explanation:

1. Calculating the area of 2 - D shapes:

• a. Circle:
• # Explanation:

Step1: Recall the area formula for a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius. Given \(r = 44\space mm\).
\(A=\pi\times(44)^{2}\)
\(A = 1936\pi\space mm^{2}\approx1936\times3.14 = 6079.04\space mm^{2}\)

• # Answer: \(A\approx6079.04\space mm^{2}\)
• b. Triangle:
• # Explanation:

Step1: Recall the area formula for a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base \(b = 18\space m\) and the height \(h = 9\space m\).
\(A=\frac{1}{2}\times18\times9\)
\(A = 81\space m^{2}\)

• # Answer: \(81\space m^{2}\)
• c. Rectangle:
• # Explanation:

Step1: Recall the area formula for a rectangle

The formula for the area of a rectangle is \(A = length\times width\). Given length \(l=85\space m\) and width \(w = 52\space m\).
\(A=85\times52\)
\(A = 4420\space m^{2}\)

• # Answer: \(4420\space m^{2}\)
• d. Composite - shape (rectangle + triangle):
• First, find the area of the rectangle part:
• # Explanation:

Step1: Recall the area formula for a rectangle

The formula for the area of a rectangle is \(A_{1}=length\times width\). Given length \(l = 96\space m\) and width \(w = 75\space m\).
\(A_{1}=96\times75=7200\space m^{2}\)

• # Answer for rectangle part: \(7200\space m^{2}\)
• Then, find the area of the triangle part:
• # Explanation:

Step1: Recall the area formula for a triangle

The base of the triangle is the same as the width of the rectangle (\(b = 75\space m\)), and the height of the triangle \(h=(96 - 75)=21\space m\). The formula for the area of a triangle is \(A_{2}=\frac{1}{2}\times base\times height\).
\(A_{2}=\frac{1}{2}\times75\times21\)
\(A_{2}=\frac{1575}{2}=787.5\space m^{2}\)

• # Answer for triangle part: \(787.5\space m^{2}\)
• Now, find the total area of the composite - shape:
• # Explanation:

Step1: Add the areas of the rectangle and the triangle

\(A = A_{1}+A_{2}\)
\(A=7200 + 787.5=7987.5\space m^{2}\)

• # Answer: \(7987.5\space m^{2}\)

1. Naming the prisms:

• a. Triangular prism:
• # Explanation:

Step1: Identify the base shape

The bases of the prism are triangles, so it is a triangular prism.

• # Answer: Triangular prism
• b. Octagonal prism:
• # Explanation:

Step1: Identify the base shape

The bases of the prism are octagons, so it is an octagonal prism.

• # Answer: Octagonal prism
• c. Rectangular prism:
• # Explanation:

Step1: Identify the base shape

The bases of the prism are rectangles, so it is a rectangular prism.

• # Answer: Rectangular prism
• d. Pentagonal prism:
• # Explanation:

Step1: Identify the base shape

The bases of the prism are pentagons, so it is a pentagonal prism.

• # Answer: Pentagonal prism

Answer:

1. Calculating the area of 2 - D shapes:

• a. Circle:
• # Explanation:

Step1: Recall the area formula for a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius. Given \(r = 44\space mm\).
\(A=\pi\times(44)^{2}\)
\(A = 1936\pi\space mm^{2}\approx1936\times3.14 = 6079.04\space mm^{2}\)

• # Answer: \(A\approx6079.04\space mm^{2}\)
• b. Triangle:
• # Explanation:

Step1: Recall the area formula for a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base \(b = 18\space m\) and the height \(h = 9\space m\).
\(A=\frac{1}{2}\times18\times9\)
\(A = 81\space m^{2}\)

• # Answer: \(81\space m^{2}\)
• c. Rectangle:
• # Explanation:

Step1: Recall the area formula for a rectangle

The formula for the area of a rectangle is \(A = length\times width\). Given length \(l=85\space m\) and width \(w = 52\space m\).
\(A=85\times52\)
\(A = 4420\space m^{2}\)

• # Answer: \(4420\space m^{2}\)
• d. Composite - shape (rectangle + triangle):
• First, find the area of the rectangle part:
• # Explanation:

Step1: Recall the area formula for a rectangle

The formula for the area of a rectangle is \(A_{1}=length\times width\). Given length \(l = 96\space m\) and width \(w = 75\space m\).
\(A_{1}=96\times75=7200\space m^{2}\)

• # Answer for rectangle part: \(7200\space m^{2}\)
• Then, find the area of the triangle part:
• # Explanation:

Step1: Recall the area formula for a triangle

The base of the triangle is the same as the width of the rectangle (\(b = 75\space m\)), and the height of the triangle \(h=(96 - 75)=21\space m\). The formula for the area of a triangle is \(A_{2}=\frac{1}{2}\times base\times height\).
\(A_{2}=\frac{1}{2}\times75\times21\)
\(A_{2}=\frac{1575}{2}=787.5\space m^{2}\)

• # Answer for triangle part: \(787.5\space m^{2}\)
• Now, find the total area of the composite - shape:
• # Explanation:

Step1: Add the areas of the rectangle and the triangle

\(A = A_{1}+A_{2}\)
\(A=7200 + 787.5=7987.5\space m^{2}\)

• # Answer: \(7987.5\space m^{2}\)

1. Naming the prisms:

• a. Triangular prism:
• # Explanation:

Step1: Identify the base shape

The bases of the prism are triangles, so it is a triangular prism.

• # Answer: Triangular prism
• b. Octagonal prism:
• # Explanation:

Step1: Identify the base shape

The bases of the prism are octagons, so it is an octagonal prism.

• # Answer: Octagonal prism
• c. Rectangular prism:
• # Explanation:

Step1: Identify the base shape

The bases of the prism are rectangles, so it is a rectangular prism.

• # Answer: Rectangular prism
• d. Pentagonal prism:
• # Explanation:

Step1: Identify the base shape

The bases of the prism are pentagons, so it is a pentagonal prism.

• # Answer: Pentagonal prism