Surface Area of Pyramid

[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 3^rd 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

 

[pappus]

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 3^rd 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


View attachment 1879

If I understand your question correctly then you are looking for the surface area of the apothem, right?

1. The surface area consists of

• 2 right triangles
• 3 trapezoids

2. Area of the 2 right triangles is A=(1/*2)* a * b with

• a = 8, b = 6 at the base triangle
• a = 4, b = 3 at the top triangle

3. Area of a trapezoid is calculated by A = (a + c)/2 * h where a and c are the parallel sides of the trapezoid.

4. I've got a total surface area of 246 cm²