SaiBook.us Geometry

Lesson Example Discussion Quiz: Class Homework

Example

Title: Surface area for Prism & Sphere

Grade: 6-a Lesson: S3-L3

Explanation: The best way to understand geometry is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

Find the height of the pentagonal prism if the total surface area of the pentagonal prism is 160 sq.cm., apothem length and base length are 6 cm. and 2 cm.

Step 1a

Given that the total surface area of a pentagonal prism (TSA) is 160 sq.cm, with an apothem length (a) of 6 cm and a base length (b) of 2 cm.

$1a$

Explanation: Given that the apothem length (a) of a pentagonal prism is 6 cm, with a base length (b) of 2 cm and a total surface area of 160 sq.cm.

Step 1b

The formula for the total surface area of a pentagonal prism is TSA = 5ab + 5bh.
Now plug the values into the formula:
160 = 5(6)(2) + 5(2)h

Explanation: TSA formula for pentagonal prism: 5ab + 5bh. Plugging values gives 160 = 5(6)(2) + 5(2)h.

Step 1c

Now solve for h:
⇒ 160 = 60 + 10h
Subtract 60 on both sides:
⇒ 10h = 100
Divide 10 on both sides of the equation:
⇒ h = 10
Therefore, the height of the pentagonal prism is 10 cm.

Explanation: In this step, solve for height(h) in the equation 160 = 60 + 10h by subtracting 60 from both sides to get 100 = 10h. Then, divide both sides by 10 to find that h = 10 cm.