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Ok I have managed to complete the questions. Thank you for the help.
1. An equilateral triangle with a side of 1 inch
Area =0.43 in
360/3 = 120
(180-120)/2
=60/2
=30
0.5tan(30°)
=0.288
1/2(1)(.288)
=0.144 x 3
=0.43 in
2. A square with a side of 2 feet
Area = 4 ft
360/4 = 90
(180-90)/2
90/2
= 45°
2/2 = 1
1tan45°=1x4
= 4 ft
3. A regular pentagon with a side of 3 centimeters
Area = 15.45 cm
360/5 = 72
(180-72)/2
108/2
= 54°
3/2
1.5
1.5tan54°
= 2.06
1/2(3)(2.06)
3.09 x 5
A = 15.45 cm
4. A regular hexagon with a side of 10 cm
Area = 433 cm
360/6 = 60
(180-60)/2
120/2
=60
10/2 = 5
5tan60° = 8.66
1/2(10)(8.66)
=43.3 x 6
A = 259.80 cm
5. A regular heptagon with a side of 7 inches.
Area = 177.87 in
360/7 = 51.42
(180-51.42)/2
128.58/2
=64.29
7/2 = 3.5
3.5tan64.29°
= 7.26
1/2(7)(7.26)
25.41 x 7
= 177.87 in
6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm.
Area = 216 cm
1/2(16+8)(18)
=216
7. A trapezoid where the height = 7 mm, base 1 = 26 mm and base 2 = 9 mm.
Area = 122.5 mm
1/2(26+9)(7)
=122.5
8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2
b1=26.2cm
1/2(19.8)=9.9
401.94/9.9=40.6
40.6-14.4=26.2
1/2(26.2+14.4)(19.8)=401.94
9.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2
height = 10
1/2(20+21) = 20.5
205/20.5 = 10
1/2(20+21)(10) = 205
10. If the area of a parallelogram is 690.84 m2 and the height is 20.2 m, what is the length of the base?
base=34.2m
690.84/20.2=34.2
1/2(34.2)(20.2)=345.42 m2
345.42(2) = 690.84
11. If the base of a rectangle is 28 cm and the area is 588 cm^2, what is the height of the rectangle?
height = 21 cm
588/28=21
1/2(28)(21)=294
294(2)=588
12. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?
area= 416 cm^2
1/2(16)(26) = 208
208(2) = 416
13. What is the area of this polygon? Show all of your calculations.
ls_XF = 53 mm ls_XV = 72 mm ls_VR = 16 mm
ls_FB = 31 mm ls_BT = 31 mm ls_EU = 47 mm
ls_UL = 31 mm ls_TL = 88 mm ls_DE = 16 mm
ls_RM = 70 mm ls_MC = 21 mm ls_DC = 70 mm
area=8014mm
since its a rectangle all the shorter sides equaled the same as the corresponding side so:
81x31 = 2728
21x70 = 1470
53x72 = 3816
2728+1470+3816=8014
14. What is the area of this rectangle? Show all of your work.
area=60
h^2=13^2-12^2
h^2=25
h=5
12x5=60
15. What is the area of this polygon? Show all of your work.
area=220
1/2(12)(10)=60
(20)(8)=160
160+60=220
Hi aquafina09,
Applying the value 1 inch,
required area is approximately 0.433 sq in.
Huh okay so different formula, but the same, (or very close) answer. Thank you!
so for #1
360/3 = 120
(180-120)/2
=60/2
=30
.5tan(30°)
=.288
1/2(1)(.288)
=.144 x 3
=0.432
Did I do this right?
Hello,
I've been having a lot of trouble with a lesson called Areas of Polygons. The lesson it gives me is really hard to
understand. Could somebody help show me how to figure these questions out?
For #1-7, calculate the area for each of the polygons described below. Round answers to the nearest hundredth and remember to include the unit of measure.
- For #3, 4, and 5, divide the polygon into triangles as shown in the lesson.
- You must show the work for any values not provided in the problem, including the height for the triangles in #1, 3, 4, and 5.
1. An equilateral triangle with a side of 1 inch
2. A square with a side of 2 feet
3. A regular pentagon with a side of 3 centimeters
4. A regular hexagon with a side of 10 cm
5. A regular heptagon with a side of 7 inches.
6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm.
7. A trapezoid where the height = 7 mm, base 1 = 26 mm and base 2 = 9 mm.
For #8 and #9, fill in the missing information for the following trapezoids. SHOW YOUR WORK to solve for the missing value.
8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2
9.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2
10. If the area of a parallelogram is 690.84 m2 and the height is 20.2 m, what is the length of the base?
11. If the base of a rectangle is 28 cm and the area is 588 cm^2, what is the height of the rectangle?
12. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?
13. What is the area of this polygon? Show all of your calculations.
ls_XF = 53 mm ls_XV = 72 mm ls_VR = 16 mm
ls_FB = 31 mm ls_BT = 31 mm ls_EU = 47 mm
ls_UL = 31 mm ls_TL = 88 mm ls_DE = 16 mm
ls_RM = 70 mm ls_MC = 21 mm ls_DC = 70 mm
14. What is the area of this rectangle? Show all of your work.
15. What is the area of this polygon? Show all of your work.
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