The net of a square pyramid is shown:

What is the surface area of the figure?

0.65 square inch 0.50 square inch 0.40 square inch 0.25 square inch

Nickolas Mar 21, 2019

#1**0 **

Square area = side x side = .5 x.5 sq in = .25 sq in

triangles areas = 4 triangles x 1/2 base x height = 4 x 1/2 x .5 x .4 = .4

total = .25 + .4 = .65 sq in

ElectricPavlov Mar 21, 2019

#3**+5 **

For this problem you can just calculate the areaa of the all the the shapes and add them together...

The two formula's you will need for this will be the area of a triangle and the area of a rectangle

*Triangle*

\(Base * Height *\frac{1}{2}\)

*Rectangle *

\(Length * with\)

*so lets calculate the area of the rectangle *

\(0.5 * 0.5 = 0.25\)

*area of thhe rectangle is 0.25 square inches*

*Now to find the area of all four triangles and as you stated they have they all have diffrent heights I will start with the triangle that has a height of 0.40 0r 0.4 and go clock wise. *

*so the area for this triangle is *

\(0.5 * 0.4 * \frac{1}{2} \)

\(0.5 * 0.4 = 0.20\)

\(0.20 * \frac{1}{2} = 0.1 \)

*The total area of this triangle is 0.10*

The next triangle is

\(0.5 * 0.5 * \frac{1}{2}\)

\(0.5 * 0.5 = 0.25\)

\(0.25 * \frac{1}{2} = 0.125\)

The total area is **0.125**

The next triangle. is I am assuming you get the Idea on how to set up so I am going to jump to the problem from here.

\(0.5 * 0.65 = 0.325\)

\(0.325 * \frac{1}{2} = 0.1625\)

total area 0.**1625 **

*The final triangle *

\(0.5 * 0.25 = 0.125\)

\(0.125 * \frac{1}{2} = 0.0625\)

0.6635 **square units. ALTHOUGH I FEEL LIKE I DID SOMETHING WRONG I WOULD GO WITH EP's ANSWER.**

HiylinLink Mar 21, 2019

#4**0 **

HL: you were spot-on through this point:

so the area for this triangle is

....

....

........

The total area of this triangle is 0.10 <-------- all 4 triangles are of the same size so 4 x .1 = .4 then add to the square

ElectricPavlov
Mar 21, 2019

#5**+7 **

Oh I se Thank you I was just curious because he has numbers at the botom and two of them are the same as the height of the other triangles so I though the other two were the ones that weren't labeled so that kind of was my reasoning for my answer....

The net of a square pyramid is shown:

What is the surface area of the figure?

0.65 square inch 0.50 square inch 0.40 square inch 0.25 square inch

I Didn't know how to include the pic so I have it like that : )

HiylinLink
Mar 21, 2019

#6**+1 **

I think the numbers at the bottom are choices for answers that the poster has.......

ElectricPavlov
Mar 21, 2019

#7**+7 **

OOOOOH Wow that really makes sense XD can't beilive I did that I could have just multiplied the triangles all together.......

HiylinLink
Mar 21, 2019