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?
(the picture of the shape looks like a pentagon but the rectangle is much longer)
total surface area=side area+base + top
side area given.
base perimeter given
assuming the triangle is regular,then each side of the triangle is 400/(10*3) or 40/3 in length.
area=sqrt(s*(s-a)(s-b)(s-c))
where a=b=c= 40/3, and s is half perimter or 20
areabase=sqrt(20 (20-40/3)^3)
=20 sqrt(2/3)^3=40/3sqrt(2/3)
check that.
then total area=400+2*40/3sqrt2/3 if the above is correct.
To find the surface area of the triangular prism, we need to calculate the areas of all its faces and then sum them up.
The triangular prism consists of three rectangular faces and two triangular faces.
1. Let's start by calculating the areas of the rectangular faces:
To find the length of each rectangular face, we know that the base perimeter is 40 inches and there are 4 sides. So, the length of each side of the rectangle is 40/4 = 10 inches.
The height of the prism is given as 10 inches. Therefore, the area of each rectangular face is length x width = 10 inches x 10 inches = 100 square inches.
Since there are three rectangular faces, the total area of the rectangular faces is 3 x 100 square inches = 300 square inches.
2. Now let's calculate the areas of the triangular faces:
The lateral surface area of the triangular prism is given as 400 square inches, which is the total surface area of the sides. This includes the area of the two triangular faces.
So, the area of each triangular face is half of the lateral surface area, 400 square inches / 2 = 200 square inches.
Since there are two triangular faces, the total area of the triangular faces is 2 x 200 square inches = 400 square inches.
3. Finally, sum up the areas of all the faces to find the total surface area of the triangular prism:
Total surface area = Area of rectangular faces + Area of triangular faces
Total surface area = 300 square inches + 400 square inches = 700 square inches.
Therefore, the surface area of the given triangular prism is 700 square inches.