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Flura [38]
3 years ago
12

Use the following image to answer the questions below. The base is a regular pentagon and the vertex is directly above the cente

r of the base:
a. If you knew the dimensions of this solid, how would you calculate the surface area?
b. How would you calculate the volume?
c. How does the volume of this pentagonal pyramid compare to the volume of a prism with a congruent pentagonal base and a congruent height?
d. What cross-sectional shapes, regular or irregular, could you get by cutting a plane through this figure? Explain your answer.

Mathematics
1 answer:
levacccp [35]3 years ago
7 0

a. The lateral area is the area of 5 congruent triangles. The strategy for computing their area will depend on the dimensions given. There are methods for computing triangle area based on side lengths, base length and height, coordinates of the points, and other dimensions. One straightforward way, given the appropriate dimensions is to multiply the slant height by the perimeter of the base, then divide that product by 2.


The base area is that of 5 congruent triangles. Again, their total area can be computed from half the product of the perimeter of the base and the apothem (height of the triangle).


The total surface area is the sum of lateral area and base area.


For example, given the apothem of the base (a) and the slant height of the side face (s), the total surface area (A) will be

... A = 5·a·tan(36°)·(a + s)


b. The volume is conventionally calculated as 1/3 of the product of the base area (B) and the height (h).

... V = (1/3)Bh


c. The volume of a prism with the same base area and height will be

... V = Bh

The volume of a pyramid is 1/3 of that.


d. A plane can intersect this pyramid to form a triangle, rectangle, trapezoid or other irregular quadrilateral, pentagon, or hexagon. The number of edges the cross-section has depends on the number of faces (including the base) the plane cuts. That number can be 3 through 6.

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What is surface area?​
schepotkina [342]
The surface area is the area of the outside of a 3D shape for example, let’s say you have a cube, a cube has 6 sides, so you have to find the area of each side and then add it up, since it’s a cube you would technically have to find the area of one side and then just multiply it by 6, that would be the easiest way to do it


Hope I helped!
8 0
3 years ago
Tulsa has 4 times as many mangoes as Julie. Tulsa bought 6 more mangoes. She now has 5 time as many mangoes as Julie . How many
vova2212 [387]

Answer:

24

Step-by-step explanation:

Let the number of mangoes owned by Tulsa be T and that by Julie be J

If Tulsa has 4 times as many mangoes as Julie then

T = 4J

Tulsa bought 6 more mangoes. She now has 5 time as many mangoes as Julie

T + 6 = 5J

Solve both equations simultaneously by substitution

4J + 6 = 5J

Collect like terms

6 = 5J- 4J

J = 6

Since

T = 4J

T = 4 * 6

= 24

Hence Tulsa had 24 mangoes at first

8 0
3 years ago
Help me out smartie pants hahahahaahahaha
MAXImum [283]

Answer:

5/8            

I had it                                                                        

4 0
3 years ago
Evaluate the expression when c=4 and d=48. d-6c​
Rama09 [41]

Answer:

24

Step-by-step explanation:

since c=4 and d=48, we can re-write this equation

48-6 x 4

48 - 24

24

5 0
3 years ago
Levens and frank shared a pizza levens ate 1/2 and frank ate 1/6 how much more did levens eat than Frank?
bezimeni [28]

Answer:

the answer is 9

Step-by-step explanation:

3 0
3 years ago
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