## Description

Task 1

A real estate company sells plots of land. The plot shown at the right costs $84,120. What is the price per square foot of the land? Explain how you found your answer.

Task 2: An arc length is a fractional part of the circumference of a circle. The area of a sector is a fractional part of the area of a circle.

The stained glass circle-head window has a 2-in. wide frame. The grills divide the semicircular glass pane into four congruent regions.

a. What is the area of the blue region? b. What is the outside perimeter of the window frame?

.

Task 3: The ratio of the perimeters and the ratio of the areas of two similar figures are related to the ratio of the corresponding measures

Regular hexagon ABCDEF has vertices at A(4, 4!3), B(8, 4!3), C(10, 2!3), D(8, 0), E(4, 0) and F(2, 2!3). Suppose the sides of the hexagon are reduced by 40% to produce a similar regular hexagon. What are the perimeter and area of the smaller hexagon rounded to the nearest tenth? Explain how you found your answer.

I have attached a copy of the actual assignment that contains pictures and the project rubric that shows everything that must be included to receive a passing grade.

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## Explanation & Answer

Attached you will find the answers for the three tasks. Please let me know if you need a clarification or edit 😀

Task 1.

Alternative 1.

We divide the land in two trapezoids. The area of a trapezoid is

defined by the equation:

1

𝐴 = × (𝑏1 + 𝑏2 ) × ℎ

2

The area of the first trapezoid is:

1

1

𝐴1 = × (125ft + 265ft) × 110ft = × (390ft) × 110ft=21450ft 2

2

2

The area of the second trapezoid is:

1

1

𝐴2 = × (150ft + 265ft) × 150ft = × (415ft) × 150ft=31125ft 2

2

2

Total Area:

𝐴 𝑇 = 𝐴1 + 𝐴2 = 21450ft 2 + 31125ft 2 = 52575ft 2

Price per square foot (PSF):

𝑇𝑜𝑡𝑎𝑙 𝑉𝑎𝑙𝑢𝑒

$84120

𝑃𝑆𝐹 =

=

= $1.60/ft 2

𝐴𝑇

52575ft 2

Alternative 2.

We calculate the area of the exterior rectangle and calculate the

difference of the orange triangles.

Area of the rectangle:

𝐴1 = 𝑏 × ℎ = 265ft × 260ft=68900ft 2

The area of the two small orange triangles:

1

1

𝐴2 = 2 × × 𝑏 × ℎ = 2 × × 70ft × 110ft=7700ft 2

2

2

The area of the big orange triangle:

1

1

𝐴3 = 2 × × 𝑏 × ℎ = 2 × × 150ft × 115ft=8625ft 2

2

2

Total Area:

𝐴 𝑇 = 𝐴1 − 𝐴2 − 𝐴3 = 68900ft 2 − 7700ft 2 − 8625ft 2 = 52575ft 2

Price per square foot (PSF):

𝑇𝑜𝑡𝑎𝑙...