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avanturin [10]
2 years ago
8

Find the total surface area of the following pyramids: A regular triangular pyramid has base edges of length 30 and height 10.

Mathematics
1 answer:
lawyer [7]2 years ago
3 0

Answer:

1130 units²

Step-by-step explanation:

SA = sum of area of 4 triangles.

All sides equal means it's an equlateral triangle, which has all angles 60)

1 in the base:

A1 = ½(30)(30)sin(60) = 225sqrt(3)

3 slant triangles:

base = 30

Height to be obtained using pythagoras theorem:

Perpendcular distance of the edge from the mid of the base = ½(distance of one vertex from the midpoint of the opposite edge)

Let the distance of a vertex form the midpoint of the edge opposite to it 'd'

30² = 15² + d²

d² = 675

d = 15sqrt(3)

d/2 = 15sqrt(3)/2

height² = 10² + [15sqrt(3)/2]²

height² = 268.75

height = sqrt(268.75) = 16.4

Area of 1 slant triangle:

A2 = ½(30)(16.4) = 246

SA = A1 + 3 A2

= 225sqrt(3) + 3(246)

= 1127.7 units²

= 1130 units² (3sf)

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uranmaximum [27]

Answer:

<u>Perimeter</u><u> </u><u>is</u><u> </u><u>1</u><u>6</u><u>x</u><u> </u><u>-</u><u> </u><u>1</u><u>0</u>

Step-by-step explanation:

{ \sf{perimeter = 2(length + width)}} \\ p = 2 \{(5x - 7) + (3x + 2) \} \\ p = 2(8x - 5) \\ p = 16x - 10

8 0
3 years ago
Oil spill spreads 25 m² every 1/6 hour how much area does the oil spill cover after two hours
Delvig [45]
1/6 of an hour is 10 minutes because there are 60 minutes in an hour so 60/6=10
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hope this helped
6 0
2 years ago
Read 2 more answers
Anna is playing a word game with tiles shaped like triangles. She needs to make a word with only those that appear to be right t
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3 years ago
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X+2y=8<br>2x-y=1<br>mathe question​
Ira Lisetskai [31]

Answer:

x = 2 and y = 3

Step-by-step explanation:

We have

x+2y = 8 -----equation (i)

2x-y = 1 -----equation (ii)

Now,

x+2y = 8

or, x = 8-2y ------equation (iii)

Again,

2x-y = 1

or, 2x = 1+y

or, 2x-1 = y

Putting the value of 'x' from equation (iii)

or, 2(8-2y)-1 = y

or, 16-4y-1 = y

or, 16-1 = y+4y

or, 15 = 5y

or, y = 15/5

or, y = 3

Putting the value of 'y' in equation (iii)

x = 8-2y

or, x = 8-(2×3)

or, x = 8-6

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Therefore, x = 2 and y = 3.

4 0
2 years ago
{HIGH PAYOUT} Can someone help by showing work on how to get to answer?
Gala2k [10]

Let's assume each line is one toothpick.

In figure 1, there is a square made out of the 4 toothpicks.

In figure 2, there are four squares made. However, the 4 four toothpicks were already used, so we don't count them twice. That gives 4 (that were used) + 3 (the new ones on the left) + 3 (new ones on top) + 3 (new ones on right). We sum them up: 4 + 3 + 3 + 3 = 13.

In figure 3 there are nine squares made. We have the 13 squares made, plus 3 on the left column, 2 on the left center column, 3, on the center column, 2 on the right center, and 3 on the right. We total them up. 13 + 3 + 2 + 3 + 2+ 3 = 26.

Let's look at the pattern.

<u>Figure #</u> <u># Toothpick</u>s

1 4

2 13

3 26

From figure 1 to 2, we added 9. From 2 to 3 we added 13. If we draw figure 4, we would add (from left to right) 3, 2, 2, 3, 2, 2, 3. That would be 17 toothpicks added, and 39 total. Let's go back to the table.

<u>Figure #</u> <u># Toothpick</u>

1 4

2 13

3 26

4 39

Now let's look at the sequence happening. As we add more, we increase by 9, then 13, then 17. For each row, we add the same number as the previous row and then add 4. Drawing Figure 5 would be too much, but we can conclude based on the pattern that 21 squares would be added. We can take this sequence as far as we need to. We want the 10th figure or term, so we apply the pattern and keep going until we get there.

<u>Figure #</u> <u># Toothpick</u>

1 4

2 13 <--- add 9

3 26 <--- add 13, the same 9 and 4 more

4 39 <--- add 17, the same 13 and 4 more

5 60 <--- add 21, the same 17 and 4 more

6 85 <-- add 25, the same 21 and 4 more

7 114 <-- add 29, the same 25 and 4 more

8 147 <-- add 33

9 184 <---- add 37

10 225 <-- add 41


Thus the 10th figure has 225 toothpicks.

5 0
3 years ago
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