# Thread: Surface Area of Pyramid

1. ## Surface Area of Pyramid

Hey ALL - I'm working on this and could really use some help. Am I even going in the right direction here? Please see Attached for Diagram:

Bottom Pyramid – Apothem is half of the height = 6cm
LA = Lateral Area = ph
P = 4s
P=4(10)=40
LA = 40(12) = 480
Slant Height = √180
LA = 1/2pL
LA = ½(40)( √180) = 268.33
SA = 268.33 + B
B = 102 = 100
SA = 368.33cm2
Top Pyramid
Pythagorean Theorem to find 3rd side
9 + 16 = C2
C = 5cm
P = 4(5cm) = 20cm
LA = 20(10) = 200
LA = ½(20)( √180) = 134.16
SA = 134.16 + B
B = 52 = 25
SA = 159.16cm2

Add Both Surface Areas = 368.33 + 159.16 = 527.49cm2

2. ## Re: Surface Area of Pyramid

Trapezoid upper face 3,4,5 rt triangle
lower face 6,8,10 rt tri
Draw a face of pyramid from base to vertex
Area of face = 1/2 slant height * base
Repeat for each face
How does the area of pyramid face compare to the trapezoid face area
Calculate the total trap.face area and add the upper trap face

3. ## Re: Surface Area of Pyramid

Originally Posted by SmokeDawg
Hey ALL - I'm working on this and could really use some help. Am I even going in the right direction here? Please see Attached for Diagram:

Bottom Pyramid – Apothem is half of the height = 6cm
LA = Lateral Area = ph
P = 4s
P=4(10)=40
LA = 40(12) = 480
Slant Height = √180
LA = 1/2pL
LA = ½(40)( √180) = 268.33
SA = 268.33 + B
B = 102 = 100
SA = 368.33cm2
Top Pyramid
Pythagorean Theorem to find 3rd side
9 + 16 = C2
C = 5cm
P = 4(5cm) = 20cm
LA = 20(10) = 200
LA = ½(20)( √180) = 134.16
SA = 134.16 + B
B = 52 = 25
SA = 159.16cm2

Add Both Surface Areas = 368.33 + 159.16 = 527.49cm2
Maybe I don't understand your question correctly but ...:

The top area is a right triangle whose right angle's legs have the lengthes 3 and 4 respectively. So it's area is 6 cm².

The base area is a right triangle whose right angle's legs have the lengthes 6 and 8 respectively. So it's area is 24 cm².

Since the height of the trapezoidal faces is 12 the area of each trapezoidal face is calculated by: A = (1/2)(a + c) * h
where a and c are the lengthes of the parallels. The total area of the three trapezoidal faces is calculated by: (15/2 + 12/2 + 9/2)*12

I've got a total surface area of 246 cm²

4. ## Re: Surface Area of Pyramid

By the way why don't you use the answer here: Surface Area of Pyramid

5. ## Re: Surface Area of Pyramid

The model will not require the area of base