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3 years ago

Find the surface area of the triangular prism below

Mathematics

1 answer:

laiz [17]3 years ago

5 0

QUESTION: To find the surface area of the triangular Prism given in the figure.

ANSWER:

$Area \: of \: Prism = 136 \: {units}^{2}$

STEP BY STEP EXPLANATION:

In a triangular Prism there are three rectangular faces and two triangular faces

As, in the given question the prism is irregular. So, it have different area of base rectangular face than that of the two side rectangular faces.

A/C to the question,

Base of triangular face = 6 unit

Height of triangular face = 4 unit

Length of side rectangular face = 7 unit

Breadth of side rectangular face = 5 unit

Length of base rectangular face = 7 unit

Breadth of base rectangular face = 6 unit

Area of triangle = $\frac{1}{2} \times base \times height$

Area of rectangle = Length × Breadth

AREA OF PRISM = 2 × AREA OF TRIANGULAR FACE + 2 × AREA OF SIDE RECTANGULAR FACE + AREA OF BASE RECTANGULAR FACE

=> Area of Prism = $2(\frac{1}{2} \times Base \: of \: triangular \: face \times Height \: of \: triangular \: face)$ + 2(Length of side rectangular face × Breadth of side rectangular face) + Length of base rectangular face × Breadth of base rectangular face

=> Area of Prism = $2( \frac{1}{2} \times 6 \times 4)$ + 2(7 × 5) + 7 × 5

=> Area of Prism = 2(3 × 4) + 2(7 × 5) + 7 × 6

=> Area of Prism = 2(12) + 2(35) + 42

=> Area of Prism = 24 + 70 + 42

=> Area of Prism = 136 units²

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Evgen [1.6K]

Answer:

$\displaystyle 8$

Step-by-step explanation:

we would like to compute the following limit

$\displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right)$

if we substitute 16 directly we'd end up

$\displaystyle = \frac{16 - 16}{ \sqrt{16} - 4}$

$\displaystyle = \frac{0}{ 0}$

which isn't a good answer now notice that we have a square root on the denominator so we can rationalise the denominator to do so multiply the expression by √x+4/√x+4 which yields:

$\displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \times \frac{ \sqrt{x} + 4 }{ \sqrt{x} + 4 } \right)$

simplify which yields:

$\displaystyle \lim_{x \to 16} \left( \frac{(x - 16)( \sqrt{x} + 4)}{ x - 16} \right)$

we can reduce fraction so that yields:

$\displaystyle \lim_{x \to 16} \left( \frac{ \cancel{(x - 16)}( \sqrt{x} + 4)}{ \cancel{x - 16} } \right)$

$\displaystyle \lim _{x \to 16} \left( \sqrt{x } + 4\right)$

now it's safe enough to substitute 16 thus

substitute:

$\displaystyle = \sqrt{16} + 4$

simplify square root:

$\displaystyle = 4 + 4$

simplify addition:

$\displaystyle = 8$

hence,

$\displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right) = 8$

6 0

3 years ago

Jonathan bought a Gucci belt in Chinatown for $35.00. The belt was on sale for ⅓ off the regular price. Then, an additional 8% w

leonid [27]

Answer:

<u>The original price of the belt was $ 59.32 and Jonathan paid $ 35 for it.</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount Jonathan paid for the belt = $ 35

Discount = 1/3 off the regular price

Coupon = additional 8% = 0.08

2. How much did the Gucci belt cost Jonathan? Show your work or explain how you know.

We assume the question is asking for the original price of the belt, then we make this calculation:

Amount Jonathan paid for the belt = (Original price - Discount) - Coupon

Replacing with the values we know:

Original price = x

35 = (x - 1/3x) - 0.08x

35 = 2/3x - 0.08x

35 = 0.67x - 0.08x

35 = 0.59x

x = 35/0.59

x = 59.32

<u>The original price of the belt was $ 59.32 and Jonathan paid $ 35 for it.</u>

4 0

3 years ago

A five-sided solid has the numbers 1, 2, 3, 4, and 5. What is the probability of rolling two five-sided number solids and gettin

Umnica [9.8K]

The answer is 1 out of 5

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3 years ago

During a certain 9-year period, the Consumer Price Index (CPI) decreased by

olga55 [171]

Answer:

deflation ,,,,

Step-by-step explanation:

<h3>I hope it's helpful for you ☺️</h3>

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3 years ago

A plant has an initial height of 2 inches and grows at a constant rate of 2 inches each month. A second plant that also grows at

Alik [6]

Answer:

Answer:4.8 monthsStep-by-step explanation:First, let's write down the information that we are given.Plant A: Initial Height: 3 in.Constant Rate of Growth (CRG): 2in/month (2 inches per month)Plant B:Initial Height: 1 in.CRG: 29in/year (29 inches per year)We can see that Plant B grows 29 inches per year, so lets convert Plant B's 'CGR' to months.Plant B - Divide by 12 (12 months in a year)29/12 in/yearNow, Lets put these into equations:Plant A: y = 2x + 3Plant B: y = 29/12 x + 1Now, set these two equations together and solve for x.2x + 3 = 29/12 x + 12 = 5/12 x4.8So, after 4.8 months, the plants will be the same height.

hope it helps you

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3 years ago