Math Is Fun Forum

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Area of polygons

Hello, I gotta find the areas of these two shapes, but I'm having a ton of trouble. I just can't figure out where to start. Can someone give me some pointers, please? Thanks.

#1: https://i.imgur.com/4PIIUjw.png
#2: https://i.imgur.com/rdP6UPM.png

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Area of polygons

hi simonmagusflies

Answers coming up, stay on line please.

Bob

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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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Area of polygons

Ok number 1:

Assuming that's a rectangle then you can use Pythagoras to work out the height.  Then it's just base x height.

Number 2:

Call the point where the 8 and 10 meet, point A, and the point where 10 and 15 meet point B.  Extend AB until the line meets the 20 line, at point C.  AC splits the polygon into a rectangle and a right angled triangle.  But you need to calculate the lengths AB and BC.

You can get BC using Pythag again and that will allow you to calculate the length and width of the rectangle and the base and height for the triangle.

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

simonmagusflies

Member

Registered: 2021-05-23

Posts: 32

Re: Area of polygons

Hello, I think I've got it, but I'm not sure if it's correct. If you don't mind, can you please check them for me?

#1. Solve the triangle with the Pythagorean theorem: a^2 + 12^2 = 13^2, a = 5. Find the area of the triangle: (5 x 12)/2 = 30. Multiply 30 by 2 because there are two triangles. The area of the rectangle is 60.

#2. Use the Pythagorean theorem to solve the triangle: 12^2 + b^2 = 15^2, get 9. Solve for the area: (12 x 9)/2 = 54. The rectangle's missing side length is 19 because the triangle's side is 9, 9 + 10 = 19, use to solve for area. 8 x 19 = 152. Add together to get 206, which is the area of the whole polygon.

Thanks!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Area of polygons

Yes to both.  Well done!

B

---

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