Height: 10 inches
Base Perimeter: 40 inches
Lateral Surface Area: 400 square inches (^^^this is the total surface area of the sides)
What is the Surface Area of the triangular prism?
total area = lateral area + area of bases
The area of the base is the area of a triangle with perimeter of 40 inches. unless you say more about the triangle, it's not possible to determine its area.
If it's an equilateral triangle, the just figure the height by using the side which is 40/3.
Or, it may be a right triangle.
i still don"t get it
me either. what is the shape of the base of the prism? Just saying it's a triangle isn't enough.
the picture of the shape looks like a pentagon but the rectangle is much longer
To find the surface area of a triangular prism, we need to calculate the areas of all the surfaces and then add them together.
A triangular prism has two triangular bases and three rectangular faces.
First, let's calculate the area of the triangular bases. The formula to find the area of a triangle is 1/2 * base * height.
Given the height of the prism is 10 inches, and the base perimeter is 40 inches, we can calculate the base length by dividing the perimeter by 3 (since a triangle has three sides). So the base length would be 40 inches / 3 = 13.33 inches (rounded to two decimal places).
Now we can calculate the area of one triangular base using the formula: 1/2 * base * height.
Area of one triangular base = 1/2 * 13.33 inches * 10 inches.
Area of one triangular base = 66.65 square inches (rounded to two decimal places).
Since there are two triangular bases, the total area of both bases would be 2 * 66.65 square inches = 133.3 square inches (rounded to one decimal place).
Next, let's calculate the area of the three rectangular faces.
Given that the lateral surface area of the prism is 400 square inches, we can subtract the areas of the bases from the lateral surface area to find the area of the three rectangular faces.
Area of three rectangular faces = Lateral surface area - Total area of both bases.
Area of three rectangular faces = 400 square inches - 133.3 square inches.
Area of three rectangular faces = 266.7 square inches (rounded to one decimal place).
Finally, to find the surface area of the triangular prism, we add up the areas of the two bases and the three rectangular faces:
Surface area of the triangular prism = Total area of both bases + Area of three rectangular faces.
Surface area of the triangular prism = 133.3 square inches + 266.7 square inches.
Surface area of the triangular prism = 400 square inches.
So, the surface area of the triangular prism is 400 square inches.