Respuesta :
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 dimension of the paper is given as: 12-inch by 8-inch
So, its area is:
[tex]\mathbf{A_1 =12 \times 8}[/tex]
[tex]\mathbf{A_1 =96}[/tex]
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]\mathbf{A_2 = 2 \times \frac 12 \times 2 \times 9 + 2 \times \frac 12 \times 3 \times 6}[/tex]
[tex]\mathbf{A_2 = 36}[/tex]
The area of the parallelogram is the difference between the areas of the paper and the four right triangles.
So, we have:
[tex]\mathbf{A_3 = A_1 - A_2}[/tex]
[tex]\mathbf{A_3 = 96 - 36}[/tex]
[tex]\mathbf{A_3 = 60}[/tex]
The area of a parallelogram is:
[tex]\mathbf{Area = Base \times Altitude}[/tex]
The base is given as 9.22
So, we have:
[tex]\mathbf{60 = 9.22\times Altitude}[/tex]
Divide both sides by 9.22
[tex]\mathbf{6.51 = Altitude}[/tex]
Rewrite as:
[tex]\mathbf{Altitude = 6.51}[/tex]
Hence, the altitude of the parallelogram is 6.51 inches
Read more about parallelograms at:
https://brainly.com/question/4100637