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2 years ago

What is the lateral surface are of this triangular prism?

Mathematics

2 answers:

exis [7]2 years ago

6 0

Answer:

96 in²

Step-by-step explanation:

Lateral surface area

= 3 rectangles

(4×8) + (3×8) + (5×8)

32 + 24 + 40

96 in²

maria [59]2 years ago

3 0

Answer:

96 inches squared

Step-by-step explanation:

The lateral area of the prism is the part that is not the bases. The bases here are the triangles, which means the lateral area will be the rectangles.

There are 3 rectangles with dimensions:

- 5 in by 8 in

- 4 in by 8 in

- 3 in by 8 in

The area of a rectangle is denoted by: A = lw, where l is the length and w is the width. Calculate the areas:

- 5 * 8 = 40

- 4 * 8 = 32

- 3 * 8 = 24

Add these up:

40 + 32 + 24 = 96

The answer is 96 inches squared.

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Precalculus Homework help please.

aniked [119]

Answer:

see explanation

Step-by-step explanation:

(5)

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ cos²x = 1 - sin²x

Given

3sin²Θ + 2cos²Θ - 2

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(6)

Using the trigonometric identity

secx = $\frac{1}{cosx}$

Consider the left side

$\frac{cosx}{1-sin^2x}$

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(7)

Using the trigonometric identity

1 + cot²x = csc²x

Given

sin²x. cot²x + sin²x ← factor out sin²x from each term

= sin²x(cot²x + 1)

= sin²x. csc²x

= sin²x × $\frac{1}{sin^2x}$ = 1

3 0

2 years ago

Solve for indicated variable. V= 1/3πr^2h solve for r

sergey [27]

$V=\frac{1}{3}\pi r^2h\\\\\frac{1}{3}\pi r^2h=V\ \ \ \ |multiply\ both\ sides\ by\ 3\\\\\pi r^2h=3V\ \ \ \ |divide\ both\ sides\ by\ \pi h\\\\r^2=\frac{3V}{\pi h}\Rightarrow\boxed{r=\sqrt{\frac{3V}{\pi h}}}$