Find the surface area of the right triangular prism. Round to the nearest tenth if necessary. The height is 2.5 cm, the length is 8 cm, and the width is 5.3 cm. I need help.
a1=5.5*2.5
=13.25 cm2
a2=5.3*8
=42.4cm2
a3=2.5*8/2
=10
then times by 2 cause to right triangles =20cm2
a4=8.38*5.3
=44.42
at=13.25+42.4+44.42+20
=120.11cm2
To find the surface area of a right triangular prism, we need to find the areas of each of its faces and add them together.
First, let's find the area of the triangular base. The base of the prism is a right triangle, so we can use the formula for the area of a right triangle, which is:
Area = 1/2 * base * height.
We are given the base as 8 cm and the height as 5.3 cm, so we can substitute those values into the formula:
Area of the triangular base = 1/2 * 8 cm * 5.3 cm.
Simplifying this, we get:
Area of the triangular base = 20.8 cm^2.
Next, let's find the area of each of the rectangular faces. The rectangular faces are the sides of the prism, and their areas can be found using the formula:
Area = length * width.
We are given the length as 8 cm, width as 5.3 cm, and the height as 2.5 cm. So we can calculate the areas of the rectangular faces using these dimensions:
Area of each rectangular face = 8 cm * 2.5 cm = 20 cm^2.
Since there are two identical rectangular faces, the total area of the two faces is:
Total surface area of the two rectangular faces = 2 * 20 cm^2.
Finally, to find the total surface area of the right triangular prism, we need to add the areas of the triangular base and the two rectangular faces together:
Total surface area = Area of the triangular base + Total surface area of the two rectangular faces.
Total surface area = 20.8 cm^2 + 2 * 20 cm^2.
Simplifying this expression, we get:
Total surface area = 20.8 cm^2 + 40 cm^2.
Adding these values, we find:
Total surface area = 60.8 cm^2.
Therefore, the surface area of the right triangular prism is 60.8 cm^2.
To find the surface area of a right triangular prism, you need to calculate the area of each face and then add them all together.
First, let's find the area of the triangular base. Since it is a right triangle, we can use the formula for the area of a triangle: (base * height) / 2. In this case, the base is 8 cm and the height is 5.3 cm, so the area of the triangular base is (8 * 5.3) / 2 = 21.2 cm^2.
Next, let's calculate the area of each rectangle face. There are three rectangular faces in a prism. The two rectangles on the sides have dimensions of 8 cm (length) by 2.5 cm (height), so the area of each side rectangle is 8 * 2.5 = 20 cm^2. The rectangle on the top/bottom has dimensions of 5.3 cm (width) by 8 cm (length), so its area is 5.3 * 8 = 42.4 cm^2.
To find the total surface area, add up the areas of all the faces: 21.2 cm^2 (triangular base) + 20 cm^2 (side faces) + 20 cm^2 (side faces) + 42.4 cm^2 (top/bottom face) = 103.6 cm^2.
So, the surface area of the right triangular prism is 103.6 cm^2.