Christian sells model, cars and planes. He has a display showcase of all of his collectors items solve this real world problem to find the surface area of the display showcase if it is the shape of a triangular prism with the following dimensions H=9 inches b=17 inches, s=12 inches, s2=12 inches, s3=17 inches, and l=10 inches.
It's 543.
what is it?
To find the surface area of the triangular prism, you need to calculate the areas of each face separately and then add them together.
First, let's determine the base of the triangular prism. Since the shape is a triangle, you can calculate its area using the formula: Area = (base x height) / 2.
The base of the triangle is formed by sides s2, s3, and l. To find the height, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, s2 and s3 form the two legs of the right triangle, so you can calculate the hypotenuse using the formula: c = √(a^2 + b^2), where a and b are the lengths of the two legs.
Let's first calculate the hypotenuse:
c = √(s2^2 + s3^2)
c = √(12^2 + 17^2)
c = √(144 + 289)
c = √433
c ≈ 20.81 inches
Next, let's find the height of the triangle, which is the perpendicular distance from the base to the top vertex of the triangular prism. In this case, the height is given as 9 inches (H).
Now you can calculate the area of the base:
Base Area = (base x height) / 2
Base Area = (l x H) / 2
Base Area = (10 x 9) / 2
Base Area = 90 / 2
Base Area = 45 square inches
Next, let's calculate the areas of the three rectangular faces of the prism.
The first rectangular face has dimensions s x H, so its area is:
Rectangular Face 1 Area = s x H
Rectangular Face 1 Area = 12 x 9
Rectangular Face 1 Area = 108 square inches
Since the second and third rectangular faces have dimensions b x H, their areas are equal to each other:
Rectangular Face 2 Area = Rectangular Face 3 Area = b x H
Rectangular Face 2 Area = Rectangular Face 3 Area = 17 x 9
Rectangular Face 2 Area = Rectangular Face 3 Area = 153 square inches
Now you can calculate the total surface area by summing up all the areas:
Total Surface Area = Base Area + (2 x Rectangular Face 1 Area) + (2 x Rectangular Face 2 Area)
Total Surface Area = 45 + (2 x 108) + (2 x 153)
Total Surface Area = 45 + 216 + 306
Total Surface Area = 567 square inches
Therefore, the surface area of the display showcase, shaped as a triangular prism, is 567 square inches.
The surface area of the display showcase is 1065 square inches.
To find the surface area of the triangular prism display showcase, we need to calculate the area of each of its faces and then add them up.
The triangular faces each have a base of 17 inches and a height of 9 inches, so the area of each triangular face is:
1/2 * base * height = 1/2 * 17 * 9 = 76.5 square inches
There are two triangular faces, so their combined area is:
2 * 76.5 = 153 square inches
The rectangular faces have dimensions of 10 inches by 12 inches and 9 inches by 12 inches. Therefore, their areas are:
10 * 12 = 120 square inches
9 * 12 = 108 square inches
There are two rectangular faces, so their combined area is:
2 * (120 + 108) = 456 square inches
To find the total surface area of the triangular prism display showcase, we add up the areas of all its faces:
Total surface area = 2 * area of triangular faces + 2 * area of rectangular faces
Total surface area = 2 * 76.5 + 2 * 456
Total surface area = 1065 square inches
Therefore, the surface area of the display showcase is 1065 square inches.