Math Is Fun Forum

kayla1dance

Member

Registered: 2018-01-10

Posts: 44

Math

Hello,

I am having some troubles in a lesson called Area of Polygons.
We are supposed to figure out the area of a polygon by cutting the polygon into triangles and finding the area from there. I am a little confused on how to do this. I know how to get the area of each of the questions with just the formula but I don't know how to do it with polygons. Below I posted the lesson. For questions 14 and 15 I can attach a link so you can view the pictures. I will do that when we get to those questions. just let me know.

Thank you so much,

Kayla

For 1-7, calculate the area for each of the polygons described below.  If the shape is a regular polygon with more than 4 sides, divide the polygon into triangles as shown in the lesson. Show your work using only formulas for 3- and 4-sided figures as your basis.  (Round answers to the nearest hundredth and remember to include the unit of measure.)

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.

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?

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?

15. What is the area of this polygon?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Math

hi Kayla,

I will show you what to do for any regular polygon.  This diagram shows a regular pentagon (5 sides).

You can see that lines radiating out from the centre divide the pentagon into 5 equal triangles.

(1) 360  ÷  5 will tell you the angle at the top of one triangle.

(2) The triangle is isosceles so if you subtract the top angle from 180 and divide the result by 2  you'll have the angle at the bottom of the triangle.

(3) The triangle is split in two so that you have a right angled triangle.  You can use basic trig. on this.  (Half the side) x tan(angle at bottom) = height of triangle.  This is the length of the dotted line.

(4) Calculate the area of the triangle using the formula half x base x height.

(5) Multiply this answer by 5 to get the total area of the pentagon.

If you give this method a try and post your answer at each stage I'll check them for you.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

kayla1dance

Member

Registered: 2018-01-10

Posts: 44

Re: Math

Hello,

I'd appreciate it if you could delete this post as well!

Thank you again,

Kayla