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Ierofanga [76]
1 year ago
8

What is the length of the apothem of the regular pentagon shown below? Round to one decimal place

Mathematics
1 answer:
DerKrebs [107]1 year ago
7 0

Answer:

A

Step-by-step explanation:

Draw a diagonal line connecting the centre to a vertex at the bottom. This makes a triangle. It is a regular pentagon so the base of that triangle is 7.6 / 2, which is 3.8. You also know that the angle from the apothem to the base is 90 degrees. You also know that you could split the centre angle into 5 triangles. 360 / 5 = 72 and we have half of it so it is 36 degrees.

Let's see what we have so far:

The base of the triangle is 3.8

The angle at the bottom is 90

The angle at the top is 36

We now have the tan and the opposite and we need the adjacent so rearrange for adjacent.

This gives you adjacent = opposite / tan(angle)

adjacent = 3.8 / tan(36)

adjacent = 5.2m

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A room is 20 feet by 25 feet with a 10-foot ceiling. If Mickey paints the walls and the ceiling, how much surface area will he c
Svetradugi [14.3K]

Answer:

1400ft²

Step-by-step explanation:

Given

Room Dimension: 20 ft by 25 ft by 10 ft

Where Length = 20 ft

Width = 25 ft

Height = 10 ft

Required

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We'll assume that the room is rectangular in shape and all 4 sides are covered.

<em>This means that Mickey will paint 4 walls and 1 ceiling.</em>

The dimension of the 2 of the 4  walls is as follows;

20ft by 10ft, 25ft by 10ft,

Because opposite sides of a rectangle are equal, the dimension of the remaining 2 walls is: 20ft by 10ft, 25ft by 10ft

Calculating the area of the 4 walls;

Area = 20ft * 10ft + 25ft * 10ft + 20ft * 10ft + 25ft * 10ft

Area = 200ft^2 + 250ft^2 + 200ft^2 + 250ft^2

Area = 900ft^2

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20ft by 25ft

Calculating the area of the ceiling

Area = 20ft * 25ft

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So, the area Micky will cover = Area of 4 walls + Area of ceiling

Total Surface Area = 900ft^2 +500ft^2

Total Surface Area = 1400ft^2

Hence, Micky will cover 1400ft²

6 0
3 years ago
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Answer:

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Step-by-step explanation:

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