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elixir [45]
3 years ago
8

Find the surface area of the following prism.

Mathematics
1 answer:
Alex3 years ago
3 0

Answer:

226 11/20 cm^2.

Step-by-step explanation:

This consists of 2 trapezoids and 4 rectangles.

Area of the 2 trapezoids = 2 * 4 *(6 1/2 + 5 1/4 ) /2

= 47 cm^2.

Area of the 4 rectangles =  4*9 + 6 1/2 * 9 +  4 1/5 * 9 + 9* 5 1/4

=  36 +  117/2 + 189/5 + 189/4

= 3591/20 cm^2

Total surface area = 47 + 3591/20

= 4531/20

= 226 11/20 cm^2.

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Given a line with a slope of1/2 and a point(6,5) which lies on that find an equation to represent that line
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Answer:

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Step-by-step explanation:

Because two points determine a line, you can draw altitude​ BD perpendicular to AC with height h. By the definition of a sine ratio, <u>sin(C) = h/a</u>, which can be rearranged into​ a·sin(C) = h​. The area of △ABC is A=1/2bh. The <u>substitution property of equality</u> can be used to write A=1/2b(a sinC), which becomes A=1/2ab(sinC) by the <u>commutative property of multiplication</u>.

___

The mnemonic SOH CAH TOA reminds you that the sine ratio is ...

  Sin = Opposite/Hypotenuse

Here, the side of the right triangle opposite angle C is designated "h", the height of ∆ABC. The hypotenuse of that right triangle is side "a". So ...

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__

The substitution property of equality lets you replace any expression with its equal. Here, we have h=a·sin(C), so we can use a·sin(C) in place of h in the formula for triangle area:

  1/2bh = 1/2ba·sin(C)

__

The commutative property of multiplication lets you rearrange the order of the factors in a product, so ...

  ba = ab

and

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