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schepotkina [342]
3 years ago
11

Find the lateral area and surface area of a regular hexagonal right prism is the base edges are 10 and the height is 12.

Mathematics
1 answer:
nadezda [96]3 years ago
3 0

Answer:

Step-by-step explanation:

a hexagonal prism is made up of two bases that are hexagons and six faces that are rectangles.

Lateral surface area, LA = Perimeter × height

Perimeter = number of sides × length of each side

Perimeter, P = 6 × 10 = 60

LA = 60 × 12 = 720 units squared

Area of each base, B = 1/2a × perimeter

Where

a = apotherm

We would determine the length of the apotherm of each base of the prism by applying the formula,

a = s/[2tan(180/n)]

Where

s = length of each side = 10

n = 6 sides

a = 10/[2tan(180/6) = 10/[2tan30)

a = 8.66

B = 1/2 × 8.66 × 60 = 259.8

Total surface area = LA + 2B

Total surface area = 720 + 2 × 259.8 = 1239.6 units squared

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We know that Mary makes 242 units of something in 11 hours of work, then her rate of work is:

R = (242 units)/(11 hours) = 22 units per hour.

Now, if she wants to make 374 units, then she needs to work for a time T, such that:

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2 years ago
The value of b when solving the equation 2 (6 + 12) = 16 is:
elena-s [515]

Answer:

Step-by-step explanation:

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8 0
3 years ago
In the picture below, ABCD is a rectangle. If the area of triangle ABE is 40, what is the area of the triangle?
MariettaO [177]

Area of the rectangle: 112

Step-by-step explanation:

Picture is missing: find it in attachment.

The area of a triangle is given by

A=\frac{1}{2}bh

where

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For triangle ABE, we know that

A = 40 (area)

h = 8 (height)

So we can find the length of the base AE:

AE=b=\frac{2A}{h}=\frac{2(40)}{8}=10

Now we observe that the base of the rectangle, AD, is the sum of AE and DE, therefore:

AD=AE+DE=10+4=14

We also know the height of the rectangle AB is 8, and that the area of a rectangle is

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Alex_Xolod [135]

Answer:

7.5

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4 0
3 years ago
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