How do you go about finding the lateral area of a trianglar prism?
Ex: The base of a triangular prism is an equilateral triangle with a perimeter of 42 cm. If the height of the prism is 10 cm, find the lateral area.
Thanks for the help in advance
Each of the three rectangular sides of the prism has an area of 14 x 10 = 140 cm^2. So there are 420 sq. cm of lateral area consisting of rectangles.
There are also two triangle sides. An equilateral triangle with 42 cm perimeter has 14 cm sides and a height of 14 sin 60 = 12.12 cm
The area of each triangular end is therefore
(1/2)x14x12.12 = 84.9 cm^2
Add 2 x 84.9 to 420 cm^2 for the answer.
To find the lateral area of a triangular prism, you need to calculate the sum of the areas of all three sides which make up the outer surface of the prism. Here's the step-by-step guide on how to find the lateral area:
1. Calculate the area of the base: In this case, the base is an equilateral triangle. The formula for the area of an equilateral triangle is A = (s^2 * √3) / 4, where "s" represents the length of one side.
Given that the perimeter of the triangle is 42 cm, divide it by 3 to find the length of each side. Therefore, s = 42 cm / 3 = 14 cm.
Plugging in the value of s into the area formula gives us A = (14^2 * √3) / 4.
2. Calculate the lateral area of one triangular side: The lateral area of one triangular side is equal to the area of the base multiplied by the height of the prism. So, multiply the value of the base area (from step 1) by the height of the prism.
The given height of the prism is 10 cm. Therefore, the lateral area of one triangular side is (14^2 * √3) / 4 * 10.
3. Calculate the total lateral area: Since the triangular prism has three identical sides, multiply the lateral area of one side by 3 to get the total lateral area.
Total lateral area = 3 * [(14^2 * √3) / 4 * 10] cm^2.
Simplifying and calculating this expression will give you the final result for the lateral area of the triangular prism.
Remember to always label your units correctly when writing down the answer.
To find the lateral area of a triangular prism, you need to find the area of each individual face and then add them together. Here's how you can find the lateral area of the given triangular prism:
1. Start by finding the area of the base. Since the base is an equilateral triangle, you can use the formula: Area = (sqrt(3) / 4) * side length^2, where the side length can be found by dividing the perimeter by 3. In this case, the perimeter is 42 cm, so the side length of the equilateral triangle is 42 cm / 3 = 14 cm.
Area of the base = (sqrt(3) / 4) * 14^2
2. Next, find the perimeter of one of the three lateral faces. Since the base is an equilateral triangle, the perimeter of each lateral face is equal to the base perimeter. Therefore, the perimeter of each lateral face is also 42 cm.
3. Now, calculate the area of one of the lateral faces using the formula: Area = perimeter * height, where the perimeter is 42 cm and the height is 10 cm.
Area of one lateral face = 42 cm * 10 cm
4. Since the triangular prism has three identical lateral faces, you need to multiply the area of one lateral face by 3 to get the total lateral area.
Total lateral area = Area of one lateral face * 3
Plug in the values from the problem and solve for the total lateral area.