Finding the area of these shapes.

S

simonmagusflies

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geo1.PNG
I'm stuck. I can't figure out how to do this. Find the height of the triangles? Solve for the height of the rectangle? I know that sin cos tan will figure somewhere but I can't figure it out. Please give me some pointers as to where to start.
geo2.PNG
I'm horrible at math and just can't figure it out. Please help.
 
simonmagusflies said:
Find the height of the triangles?
Click to expand...
Hi Simon. Yes, for the top shape, find the height of one triangle (they're both the same). These two exercises don't require trigonometry. Are you taking a trig class? The shapes involved have simple area formulas. I'll use those formulas.

The top shape is a rectangle. Its base measures 12, and you need to calculate its height (to use in the area formula below).

The height of the rectangle is the same as the height of each right triangle. Use the Pythagorean Theorem to find the height.

Rectangle Area = Base * Height

(The asterisk is a multiplication sign)

I know that sin cos tan will figure somewhere
Click to expand...
Not this time. We can extend the side labeled 10, to divide the bottom shape into a rectangle and a right triangle. We can add those two areas.

oddSH.JPG

Triangle Area = 1/2 * Base * Height

The order of steps is:

1) Get the value of x from looking at the diagram

2) Calculate the value of y from x+y=20

3) Calculate the triangle height (green) using Pythagorean Theorem

4) Use the green side, to calculate the rectangle's other dimension

5) Calculate the rectangle area by formula

6) Calculate the triangle area by formula

7) Combine those two areas, to get the total area

If you get stuck, please show what you tried.

?
 
Otis said:
Hi Simon. Yes, for the top shape, find the height of one triangle (they're both the same). These two exercises don't require trigonometry. Are you taking a trig class? The shapes involved have simple area formulas. I'll use those formulas.

The top shape is a rectangle. Its base measures 12, and you need to calculate its height (to use in the area formula below).

The height of the rectangle is the same as the height of each right triangle. Use the Pythagorean Theorem to find the height.

Rectangle Area = Base * Height

(The asterisk is a multiplication sign)


Not this time. We can extend the side labeled 10, to divide the bottom shape into a rectangle and a right triangle. We can add those two areas.

View attachment 28728

Triangle Area = 1/2 * Base * Height

The order of steps is:

1) Get the value of x from looking at the diagram

2) Calculate the value of y from x+y=20

3) Calculate the triangle height (green) using Pythagorean Theorem

4) Use the green side, to calculate the rectangle's other dimension

5) Calculate the rectangle area by formula

6) Calculate the triangle area by formula

7) Combine those two areas, to get the total area

If you get stuck, please show what you tried.

?
Click to expand...
Oh, jeez, the Pythagorean theorem!!! Me forgetting about its existence is becoming a common motif in my math career haha. Thanks for the help!
 
#1) Is the first one 60? The Pythagorean theorem tells me that the height of the rectangle is 5 (5^2 + 12^2 = 13^2). So the area of one of them is (5 x 12)/2 = 30, then multiply 30 by 2 because there are two triangles, and I get 60.

#2) Okay, so the base of the triangle is 9 (12^2 + 9^2 = 15^2). The area of the triangle is 54 [(12 x 9)/2]. So the rectangle is 8 x 19 (since the triangle base is 9, 9 + 10?) = 152. So the area of the shape is 206?
 
The reason that triangles are studied so intensively in geometry is that any plane figure enclosed in straight lines can be broken up into distinct triangles.
 
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