Math Is Fun Forum

hi demha

I assume you are asked for the areas here. 

1. An equilateral triangle with a side of 1 inch - Answer: A
A 0.43 sq in
B 0.56 sq in
C 0.89 sq in
D 0.23 sq in
E 0.19 sq in
F 0.54 sq in

Correct. 

2. A square with a side of 2 feet - Answer: B
A 9 sq ft
B 4 sq ft
C 2 sq ft
D 7 sq ft
E 3 sq ft
F 8 sq ft

Correct. 

3. A regular pentagon with a side of 3 centimeters - Answer: F
A 23.01 sq cm
B 12.34 sq cm
C 39.17 sq cm
D 9.46 sq cm
E 34.21 sq cm
F 15.48 sq cm

Correct. 

4. A regular hexagon with a side of 10 cm - Answer: D
A 641.25 sq cm
B 194.45 sq cm
C 361.25 sq cm
D 259.81 sq cm
E 105.22 sq cm
F 453.01 sq cm

Correct. 

5. A regular heptagon with a side of 7 inches. ***need help understanding how to solve***
A 178.06 sq in
B 294.16 sq in
C 169.21 sq in
D 358.91 sq in
E 157.36 sq in
F 277.91 sq in

How did you do the previous ones?  I'm doing them like this:  (i) 360/7 to get the central angle for one of 7 identical triangles. (ii) Split this angle in half to create a right angled triangle (iii) Use tan to get the height of the triangle (iv) half base x height for the area of one (v) x by 7 to get area of heptagon 

6. A trapezoid where the height is 18 cm, base 1 = 16 cm and b2 = 8 cm. - Answer: C
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 230 sq cm
E 280.9 sq cm
F 510 sq cm

Correct. 

7. A trapezoid where the height = 7 mm, base 1    = 26 mm and base 2 = 9 mm. - Answer: B
A 178.06 sq mm
B 122.5 sq mm
C 216 sq mm
D 230 sq mm
E 28.9 mm
F 510 mm

Correct. 

Fill in the missing information for the following trapezoids:

8.
height = 19.8 cm
b1 = ________
b2 = 14.4 cm
area = 401.94 cm2 - Answer: A
A 26.2 cm
B 12.5 cm
C 216 cm
D 23 cm
E 28.9 cm
F 51 cm

Correct. 

9.
height = 23 mm
b1 = 23 mm
b2 = ________
area = 529 mm2 - Answer: D
A 78.06 sq mm
B 22.5 sq mm
C 21.6 mm
D 23 mm
E 28.9 mm
F 30 mm^2

Correct. 

10.
height = ________
b1 = 20 cm
b2 = 21 cm
area = 205 cm2 - Answer: D
A 17.06 cm
B 12.5 sq cm
C 26 cm
D 10 cm
E 28.9 cm
F 50 cm^2

Correct. 

11.
height = 28.9 m
b1 = 26.9 m
b2 = ________
area = 806.31 m^2 - Answer: E

A 17.06 sq m
B 15 m
C 46 m
D 23 m
E 28.9 m
F 51 m

Correct. 

12. If the area of a parallelogram is 690.84 m^2 and the height is 20.2 m, what is the length of the base? - Answer: D
A 78.06 m
B 22.5 m
C 216 m
D 34.2 m
E 28.9 m
F 51 m

Correct. 

13. If the base of a rectangle is 28 cm and the area is 588 cm^2, what is the height of the rectangle? - Answer: E

A 17.06 cm
B 122.5 sq cm
C 216 sq cm
D 23 cm
E 21 cm
F 51 cm^2

Correct. 

14. If the height of a rectangle is 26.1 m and the base is 17.3 m, what is the area of the rectangle? - Answer: A
A 451.53 m^2
B 122.5 m^2
C 216 m^2
D 430 m^2
E 289 m^2
F 510 m^2

Correct. 

15. If the height of a parallelogram is 34 cm and the base is 15 cm, what is the area of the parallelogram? - Answer: F
A 178.06 cm^2
B 122.5 cm^2
C 216 cm^2
D 230 cm^2
E 289 cm^2
F 510 cm^2

Correct. 

16. What is the area of a parallelogram with height 26 cm, base 16 cm, and side length 28 cm?***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 416 cm^2
E 28.9 cm
F 510 cm^2

You only need two measuements.  They have given you an extra measurement just to make sure you know which two to multiply together. 

17. What is the area of a regular octagon with a side of 6 cm? ***need help understanding how to solve***
A 178.06 sq cm
B 122.5 sq cm
C 216 sq cm
D 23 cm^2
E 173.82 cm^2
F 510 cm^2

Split this into 8 triangles.  The angle at the top of each triangle is 360/8 and then you need to half this to make a right angle for the tangent calculation. 

18. What is the area of this polygon?***need help understanding how to solve***

You can split this polygon onto three rectangles.  (see picture below)  You will have to use the information to work out the length and width of each part and then add up the areas.

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

A 8014 mm2
B7030 mm2
C6027 mm2
D5478 mm2
E 1782 mm2
F 1225 mm2

19. What is the area of this rectangle?***need help understanding how to solve***

Use Pythagoras to work out the height of the rectangle.

A 17.06 sq units
B60 sq units
C21.6 sq units
D53 sq units
E 28.9 sq units
F 51 sq units

20. What is the area of this polygon?***need help understanding how to solve***

My picture below shows how you can split this shape into a rectangle and a triangle.  You will also need to use Pythag. to get the length of the red line.

A 178 sq units
B129 sq units
C230 sq units
D240 sq units
E 219 sq units
F 206 sq units

Hope that helps 

Bob