Geometry:Area Project

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Mathematics

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10 To solve these problems you will pull together many concepts and skills that you have studied about area and perimeter of polygons and circles. Pull It All Together Measurement You can use formulas to find areas of polygons. 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. 125 ft 260 ft 150 ft 265 ft Measurement 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. Task 2 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? 6 in. 28 in. Similarity The ratio of the perimeters and the ratio of the areas of two similar figures are related to the ratio of the corresponding measures. Task 3 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. Chapter 10 Pull It All Together 675
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Explanation & Answer

Hi! mayad!! I'm ready, these are your answers 😬 :

-Task 1:
First we will divide the polygon as follows:

Now we will calculate the areas of the 3 triangles (A2, A3 and A5) and then the areas of the square
A4 and the rectangle A1.
For A2 and A3:
If we join both triangles together we will get a single triangle height 260 ft -150 ft and base 265 ft 125 ft. So your area is given by:
𝐴23 =

110 · 140
= 7700 𝑓𝑡 2
2

For A5:
The A5 area is only the area of a rectangle triangle given by the multiplication of its legs divided by
2:
𝐴5 =

150 · (265 − 150)
= 8625 𝑓𝑡 2
2

For A4:
A4 is a square, and its area is given by:...


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