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3 years ago

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SOMEONE PLS PLS TELL ME THR RIGHT ANSWER AND HOW TODO IT PLLLLLSS Mary has a toy which is in the shape of a right prism with tri

angular bases. The sides of its bases are each 4 feet and its approximate height is 3.5 feet. The length of the prism between the bases is 10 feet. What is the approximate surface area of this right prism?

1 answer:

Firlakuza [10]3 years ago

4 0

Answer: surface area = 142.2 feet²

Step-by-step explanation:

The right prism has 2 triangular faces whose base is 4 feet and the height is 3.5 feet. The formula for determining the area of each is expressed as

Area = 1/2 × base × height

Area of both faces = 2 × 1/2 × 4 × 3.5 = 14 ft²

Considering the rectangular sides, Area of the base is 4 × 10 = 40 ft²

Area of the end is 3.5 × 10 = 35 ft²

To determine the width of the rectangular top, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Width = hypotenuse

Opposite side = 3.5

Adjacent side = 4

Width² = 3.5² + 4² = 28.25

Width = √28.25 = 5.32 feet

Area of rectangular top = 5.32 × 10 = 53.2 feet

Therefore, the approximate surface area of this right prism is

14 + 40 + 35 + 53.2 = 142.2 feet²

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COMPUTE<br><br> 3 ( 2 1/2 - 1 ) + 3/10

Juli2301 [7.4K]

Answer:

<h3> $\boxed{ \frac{24}{5} }$ </h3>

Step-by-step explanation:

$\mathsf{3(2 \frac{1}{2} - 1) + \frac{3}{10} }$

Convert mixed number to improper fraction

$\mathrm{3( \frac{5}{2} - 1) + \frac{3}{10} }$

Calculate the difference

⇒ $\mathrm{3( \frac{5 \times 1}{2 \times 1} - \frac{1 \times 2}{1 \times 2} }) + \frac{3}{10}$

⇒ $\mathrm{ 3 \times( \frac{5}{2} - \frac{2}{2}) } + \frac{3}{10}$

⇒ $\mathrm{3 \times ( \frac{5 - 2}{2} ) + \frac{3}{10} }$

⇒ $\mathrm{3 \times \frac{3}{2} + \frac{3}{10} }$

Calculate the product

⇒ $\mathrm{ \frac{3 \times 3}{1 \times 2} + \frac{3}{10} }$

⇒ $\mathrm{ \frac{9}{2} + \frac{3}{10}}$

Add the fractions

⇒ $\mathsf{ \frac{9 \times 5}{2 \times 5} + \frac{3 \times 1}{10 \times 1} }$

⇒ $\mathrm{ \frac{45}{10} + \frac{3}{10} }$

⇒ $\mathrm{ \frac{45 + 3}{10 } }$

⇒ $\mathrm{ \frac{48}{10} }$

Reduce the numerator and denominator by 2

⇒ $\mathrm{ \frac{24}{5} }$

Further more explanation:

<u>Addition </u><u>and </u><u>Subtraction</u><u> </u><u>of </u><u>like </u><u>fractions</u>

While performing the addition and subtraction of like fractions, you just have to add or subtract the numerator respectively in which the denominator is retained same.

For example :

Add : $\mathsf{ \frac{1}{5} + \frac{3}{5} = \frac{1 + 3}{5} } = \frac{4}{5}$

Subtract : $\mathsf{ \frac{5}{7} - \frac{4}{7} = \frac{5 - 4}{7} = \frac{3}{7} }$

So, sum of like fractions : $\mathsf{ = \frac{sum \: of \: their \: number}{common \: denominator} }$

Difference of like fractions : $\mathsf{ \frac{difference \: of \: their \: numerator}{common \: denominator} }$

<u>Addition </u><u>and </u><u>subtraction</u><u> </u><u>of </u><u>unlike </u><u>fractions</u>

While performing the addition and subtraction of unlike fractions, you have to express the given fractions into equivalent fractions of common denominator and add or subtract as we do with like fractions. Thus, obtained fractions should be reduced into lowest terms if there are any common on numerator and denominator.

For example:

$\mathsf{add \: \frac{1}{2} \: and \: \frac{1}{3} }$

L.C.M of 2 and 3 = 6

So, ⇒ $\mathsf{ \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} }$

⇒ $\mathsf{ \frac{3}{6} + \frac{2}{6} }$

⇒ $\frac{5}{6}$

Multiplication of fractions

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term.

When any number or fraction is divided by a fraction, we multiply the dividend by reciprocal of the divisor. Let's consider a multiplication of a whole number by a fraction:

$\mathsf{4 \times \frac{3}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6}$

Multiplication for $\mathsf{ \frac{6}{5} \: and \: \frac{25}{3} }$ is done by the similar process

$\mathsf{ = \frac{6}{5} \times \frac{25}{3} = 2 \times 5 \times 10}$

Hope I helped!

Best regards!

5 0

3 years ago