Answer:
54
Step-by-step explanation:
Use PEMDAS
1. 6 x 6 + 12 + 3 x 2 (multiply 6 and 6)
2. 36 + 12 + 3 x 2 (multiply 3 and 2)
3. 36 + 12 + 6 (combine like terms, so add them)
4. 54 (final answer)
Answer:
The formula for the area of the triangle is:
When <em>x</em> = 3, the area is 216 square centimeters.
When <em>x </em>= 2.4, the area is 138.24 square centimeters.
And when <em>x</em> = 5, the hypotenuse of the triangle is 50 centimeters.
Step-by-step explanation:
We are given a right triangle with a height of 8<em>x</em> and a base of 6<em>x</em>.
The area of a triangle is given by the formula:
So, by substitution:
When <em>x </em>= 3, the area will be:
And when <em>x</em> = 2.4, the area will be:
When <em>x </em>= 5, the height will be 8(5) = 40 cm and the base will be 6(5) = 30 cm.
By the Pythagorean Theorem:
So:
The hypotenuse will be:
Answer:
840cm
Let Me Know If This Is Correct I Always Want To Improve!
Thanks :)
<span> i only know PART B
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I'm not sure how you were taught, so I'll show work for different methods to get the same answer.
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Method 1: Solving for the lateral surface area of the triangular prism (not using volume)
Note that for the triangular prism:
**DON'T include the 2 triangular bases. DO include the 3 rectangular sides**
*lateral surface area does not include the area of the bases*
*lateral surface area just includes the lateral faces*
formula: (a + b + c)(h)
[a, b, c still using the values from PART A; h being your height from PART A]
Plug them into the above formula:
(10 + 13 + 13)(20) -> (10 + 26)(20) -> (36)(20) = 720
=> Your lateral surface area is 720.
(If you forget to exclude the area of the bases, you will get the surface area of 840)
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Method 2: Solving for the lateral surface area of the triangular prism (using volume)
Note that we will be using surface area, height, and volume to find the lateral area this time.
formula: A - 2 (V/h)
[A is the surface area; V is the given volume; h is the height from PART A]
Before we can plug things into the above formula, we need to find the surface area.
Since we have already found the lateral surface area (the area of the 3 rectangular sides), we just have to solve for the area of the bases (the area of the 2 triangles).
(Area of a triangle = (1/2)b*h or (0.5)(b*h) -> one-half of the base times the height
We can do this 2 ways:
1) Using our base value from PART A which is 5, and our height from PART A
which is 12
1/2(5*12) -> 1/2(60) -> 30.
Because we split that triangle in half in PART A, there are 4 triangles (2 in
each base).
So 30(4) = 120.
2) Using the whole base of the triangle which is 10, and the height from PART A
which is 12
1/2(10*12) -> 1/2(120) -> 60.
Since this time we used each whole base, instead of splitting them, there are
only 2
triangles (1 per base).
So 60(2) = 120.
Both ways gave you the same answer of 120.
Now add the lateral surface area and the area of the bases.
720 + 120
720 + 120 = 840.
840 is your surface area.
With that, you can now plug things into the formula.
A - 2 (V/h) -> 840 - 2 (1200/20) = 720
=> Your lateral surface area is 720.
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Both Method 1 & Method 2 get you a lateral surface area of 720.
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The approx. amount of cardboard used for the sides (aka lateral faces[aka rectangular sides]) of the candy box is 720.</span>
