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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.

A parallelogram is shown. An altitude is drawn from one point to the opposite side to form a right angle. The length of the base is 9.22 inches.

The resulting parallelogram has a base of approximately 9.22 inches.

Complete the following steps to calculate the altitude of the parallelogram using area methods.

The area of the sheet of paper is
square inches.

The combined area of the triangle cutouts is
square inches.

The area of the parallelogram is
square inches.

The altitude of the parallelogram rounded to two decimals is
square inches.

Respuesta :

MrRoyal

The area of a shape is the amount of space it occupies.

  • The area of the paper is 96 square inches
  • The combined area of the triangle cutouts is 36 square inches
  • The area of the parallelogram is 60 square inches
  • The altitude of the parallelogram is 6.51 inches

The area of the paper

The dimension of the paper is given as: 12-inch by 8-inch

So, its area is:

[tex]Area = 12 * 8[/tex]

[tex]Area = 96[/tex]

Hence, the area of the paper is 96 square inches

The area of the triangles

The dimensions of the 4 right triangles are: Two 2 inches by 9 inches, and two 3 inches by 6 inches

So, the combined area is:

[tex]Area = 0.5(2 * 2 * 9 + 2 * 3 * 6)[/tex]

[tex]Area = 36[/tex]

Hence, the combined area of the triangle cutouts is 36 square inches

The area of the parallelogram

The area of the parallelogram is the difference between the areas of the paper and the four right triangles.

So, we have:

[tex]Area = 96 - 36[/tex]

[tex]Area = 60[/tex]

Hence, the area of the parallelogram is 60 square inches

The altitude of the parallelogram

The base is given as 9.22

So, we have:

[tex]Area = Base * Altitude[/tex]

This gives

[tex]60 = 9.22* Altitude[/tex]

Divide both sides by 9.22

[tex]Altitude = 6.51[/tex]

Hence, the altitude of the parallelogram is 6.51 inches

Read more about parallelograms at:

https://brainly.com/question/4459854

acavazos4p09b68

Answer:

96, 36, 60, 6.51.

Step-by-step explanation:

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