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Complete the following steps to calculate the altitude of the parallelogram using area methods. The area of the sheet of paper i

stiks02 [169]

Based on the calculations, we have the following:

The area of the sheet of paper is 96 square inches.
The combined area of the triangle cutouts is equal to 36 square inches.
The area of the parallelogram is equal to 60 square inches.
The altitude of the parallelogram is equal to 6.51 square inches.

<u>Given the following data:</u>

Dimension of paper = 12-inch by 8-inch.

<h3>How to calculate the paper's area.</h3>

Mathematically, the area of the paper is given by this formula:

$Area = length \times breadth\\\\Area = 12 \times 8$

Area = 96 square inches.

<u>For the four (4) right triangles:</u>

Dimension 1 = 2 inches by 9 inches.

Dimension 2 = 3 inches by 6 inches.

Therefore, the combined area of the triangle cutouts is given by:

$A_2= (2 \times \frac{1}{2} \times 2 \times 9) + 2 \times \frac{1}{2} \times 3 \times 6\\\\A_2=18+18\\\\A_2=36\;in^2$

<h3>The area of the parallelogram.</h3>

This would be determined by subtracting the area of the four (4) right triangles from the areas of the paper as follows:

$P = A_p -A_2\\\\P=96-36$

P = 60 square inches.

<h3>The altitude of the parallelogram.</h3>

$P = base \times altitude\\\\Altitude =\frac{P}{base} \\\\Altitude =\frac{60}{9.22}$

Altitude = 6.51 square inches.

Read more on parallelogram here: brainly.com/question/4459854

<u>Complete Question:</u>

A parallelogram is cut out of a 12-inch by 8-inch sheet of paper. There are four right triangle remnants. Two have the dimensions 2 inches by 9 inches, and the other two have the dimensions 3 inches by 6 inches. The resulting parallelogram has a base of approximately 9.22 inches.

8 0

2 years ago

Read 2 more answers

What is the median of these data? 48, 60, 22, 84, 36.

Setler [38]

Answer:

48

Explanation:

You just put the numbers in order from least to greatest and its the middle one. if there's an even amount of numbers, you add the middle two and divide by 2

7 0

2 years ago

Determine the empirical formula of a compound containing 47. 37 grams of carbon, 10. 59 grams of hydrogen, and 42. 04 grams of o

Effectus [21]

Considering the definition of empirical formula, the empirical formula is C₃H₈O₂ and the molecular formula is C₉H₂₄O₆.

<h3>Definition of empirical formula</h3>

The empirical formula is the simplest expression to represent a chemical compound, which indicates the elements that are present and the minimum proportion in whole numbers that exist between its atoms, that is, the subscripts of chemical formulas are reduced to the most integers. small as possible.

<h3>Empirical formula in this case</h3>

In this case, you have:

Carbon (C): 47.37 grams
Hydrogen (H): 10.59 grams
Oxygen (O): 42.04 grams

Then it is possible to calculate the number of moles of each atom in the molecule, taking into account the corresponding molar mass:

Carbon (C): $\frac{47.37 grams}{12 \frac{g}{mole} }$ = 3.95 moles
Hydrogen (H): $\frac{10.59 grams}{1 \frac{g}{mole} }$ = 10.59 moles
Oxygen (O): $\frac{42.04 grams}{16 \frac{g}{mole} }$ = 2.63 moles

The empirical formula must be expressed using whole number relationships, for this the numbers of moles are divided by the smallest result of those obtained. In this case:

Carbon (C): $\frac{3.95 moles}{2.63 moles }$ = 1.5
Hydrogen (H): $\frac{10.59 moles}{2.63 moles }$ = 4
Oxygen (O): $\frac{2.63 moles}{2.63 moles }$ = 1

Finally, since in the empirical formula the numbers of moles must be expressed in whole numbers, the ratio of atoms is multiplied by some number with which everything is obtained in simple whole numbers (in this case by 2):

Carbon (C): 1.5× 2= 3
Hydrogen (H): 4× 2= 8
Oxygen (O): 1× 2= 2

Therefore the C: H: O mole ratio is 3: 8: 2

Finally, the empirical formula is C₃H₈O₂.

<h3>Molecular formula</h3>

To obtain the molecular formula you must relate its molecular weight (PMc) with the molecular weight of the empirical formula (PMfe).

PMfe= PM (C₃H₈O₂)= 76 g/mole

The molar mass of the compound (PMc) was determined to be 228.276 g/mol. Dividing this mass PMc by the molar mass of the empirical formula PMfe gives:

228.276 g/mol ÷ 76 g/mole= 3

This means that in the molecular formula there are 3 unit formulas (empirical formulas), so it is necessary to multiply the number of all atoms by 3.

Then, the molecular formula is C₉H₂₄O₆.

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3 0

2 years ago