A net of a triangular prism is shown below.
5m
12m
12m
13m
13m
5m
What is the surface area, in square meters, of the triangular prism?
Please I need help this is for the unit 2 lesson 15 math portfolio.
Well, I could give you the serious math explanation, but why be serious when we can have some fun? So, let's get "triangularly prismatical"!
To find the surface area of a triangular prism, you'll need to add up the areas of all the faces. But don't worry, I'm not going to make you calculate individual areas by hand. That would be "tri-some".
So, let's use the "shortcut" method that lazy clowns like me love.
First, find the area of one of the triangles on either end of the prism. Since they are isosceles triangles with base 5m and height 12m, using the formula for the area of a triangle (A = 1/2 × base × height), the area of each triangle is 30 square meters.
Now, let's move on to the three rectangular faces. Each face has a length of 12m and a height of 13m, so their areas are 12m × 13m = 156 square meters each. Since there are three of them, that's a total of 468 square meters.
Finally, add the areas of the two triangular and three rectangular faces together: 30 square meters + 30 square meters + 468 square meters = 528 square meters.
And there you have it! The surface area of the triangular prism is 528 square meters. Now, if only we could use this knowledge to solve practical clown problems, like calculating the amount of whipped cream needed for a pie fight...
To find the surface area of a triangular prism, we need to calculate the area of each face and then add them together.
The triangular prism has two triangular faces and three rectangular faces.
1. Triangular Faces:
The triangular faces have base and height measurements given in the net. Let's calculate the area of each triangle.
a) Triangle 1:
Base = 5m
Height = 12m
Area = (1/2) * base * height = (1/2) * 5m * 12m = 30m²
b) Triangle 2:
Base = 13m
Height = 5m
Area = (1/2) * base * height = (1/2) * 13m * 5m = 32.5m²
2. Rectangular Faces:
The rectangular faces have length, width, and height measurements given in the net. Let's calculate the area of each rectangle.
a) Rectangle 1:
Length = 13m
Width = 12m
Area = length * width = 13m * 12m = 156m²
b) Rectangle 2:
Length = 5m
Width = 12m
Area = length * width = 5m * 12m = 60m²
c) Rectangle 3:
Length = 5m
Width = 13m
Area = length * width = 5m * 13m = 65m²
Now, let's add up the areas of each face to find the total surface area.
Total Surface Area = Area of Triangular Faces + Area of Rectangular Faces
= (30m² + 32.5m²) + (156m² + 60m² + 65m²)
= 329.5m²
Therefore, the surface area of the given triangular prism is 329.5 square meters.
To find the surface area of a triangular prism, we need to calculate the area of each face and then sum them up.
The triangular prism has 2 congruent triangular faces on either end and 3 rectangular faces on the sides.
Let's calculate the area of each face:
1. Triangular Faces:
The base of each triangular face is a right triangle with legs measuring 5m and 12m. We can use the formula for the area of a right triangle:
Area = (base * height) / 2
Area of each triangular face = (5m * 12m) / 2 = 60m²
Since there are 2 congruent triangular faces, the total area is 2 * 60m² = 120m².
2. Rectangular Faces:
The length of each rectangular face is 13m (the longer side of the triangular prism), and the width is 5m (the shorter side of the triangular prism). We can use the formula for the area of a rectangle:
Area = length * width
Area of each rectangular face = 13m * 5m = 65m²
Since there are 3 rectangular faces, the total area is 3 * 65m² = 195m².
Finally, to find the total surface area of the triangular prism, we add the area of the triangular faces and the area of the rectangular faces:
Total surface area = Area of triangular faces + Area of rectangular faces
= 120m² + 195m²
= 315m²
Therefore, the surface area of the triangular prism is 315 square meters.