The surface area of the triangular prism is 686.6 cm².
Step-by-step explanation:
Step 1:
The volume of a triangular prism can be determined by multiplying its area of the triangular base with the length of the prism.
The base triangle has a base length of 10 cm and assume it has a height of h m.
The volume of the prism
The height of the triangle is 8.66 cm.
Step 2:
The surface area of the triangle is obtained by adding all the areas of the shapes in the prism. There are 2 triangles and 3 rectangles in a triangular prism.
The triangles have a base length of 10 cm and a height of 8.66 cm. A triangles area is half the product of its base length and height.
The rectangles all have a length of 20 cm and a width of 10 cm. The area of a rectangle is the product of its length and width.
The area of the 2 triangles ![= 2 [\frac{1}{2} (10)(8.66)] = 86.6.](https://tex.z-dn.net/?f=%3D%202%20%5B%5Cfrac%7B1%7D%7B2%7D%20%2810%29%288.66%29%5D%20%3D%2086.6.)
The area of the 3 rectangle ![= 3[(20)(10)] = 600.](https://tex.z-dn.net/?f=%3D%203%5B%2820%29%2810%29%5D%20%3D%20600.)
Step 3:
The surface area of the triangular prism 
The surface area of the prism is 686.6 cm².
A) Tangent is positive in Quadrant I.
Since sine and cosine are both positive in Quadrant I and tangent is the ratio of sine to cosine, tangent is positive in Quadrant I
For the given sentences, the algebraic expressions are:
a) N = 110*c - 300
b) N = 12*b
<h3>
How to get the algebraic expressions?</h3>
For the first statement:
A 3-digit number, where the tens digit is c, can be written as:
N = 100*a + 10*c + b
Then the hundreds digit is a, and here we know that is 3 less than the tens digit, then:
a = c - 3
The ones digit is b, here we know that it is 0, then b = 0.
Replacing that in our number we get:
N = 100*(c - 3) + 10*c = 110*c - 300
N = 110*c - 300
That is the algebraic expression.
b) A two-digit number can be written as:
N = b*10 + a
Where b is the tens digit and a is the ones digit.
Here we know that the units digit is twice as bit as the tens digit, then:
a = 2b
Replacing that we get:
N = b*10 + a = b*10 + 2b = 12*b
N = 12*b
That is the algebraic expression.
If you want to learn more about algebraic expressions:
brainly.com/question/4541471
#SPJ1
u have to multiply both of the numbers
