To calculate the surface area of the triangular prism, we need to find the area of each of the 5 faces and then sum them up.
1. The area of the rectangle on the left:
Area = length x width = 4 cm x 3 cm = 12 cm²
2. The area of the square (middle face, shown as a dashed line):
Area = side x side = 3 cm x 3 cm = 9 cm²
3. The area of the rectangle on the right:
Area = length x width = 5 cm x 3 cm = 15 cm²
4. The area of the two right triangles:
Each triangle has an area of 1/2 base x height = 1/2 x 3 cm x 4 cm = 6 cm²
Therefore, the total area of both triangles is 12 cm²
5. The areas of the two triangular faces:
The base of the triangle is the same as the length of the rectangle (4 cm), and the height is the perpendicular side of the right triangle (4 cm). Therefore, the area of each triangle is 1/2 x 4 cm x 4 cm = 8 cm²
Since there are two triangular faces, the total area of both is 16 cm²
Summing up the areas of all 5 faces:
12 cm² (left rectangle) + 9 cm² (square) + 15 cm² (right rectangle) + 12 cm² (two right triangles) + 16 cm² (two triangular faces) = 64 cm²
Therefore, the surface area of the shown net for the triangular prism is 64 cm².
Use the image to answer the question.
An illustration shows a two-dimensional net of a triangular prism with all of its sides open and visible. The net appears as a rectangle, a square, and another rectangle joined horizontally next to each other. The width of the two rectangles and the side of the square measure 3 centimeters. The length of the left rectangle is 4 centimeters. The side of the middle square, drawn in a dashed line, is 3 centimeters. The length of the right rectangle is 5 centimeters. Two right triangles adjoin the middle square at the top and bottom, with each perpendicular side measuring 4 centimeters and each hypotenuse measuring 5 centimeters.
What is the surface area of the shown net for a triangular prism?
3 answers
wrong
I apologize for the mistake. Let's try again:
The net of the triangular prism consists of 5 faces:
1. Two congruent triangular faces with base 4 cm and height 4 cm.
2. Two rectangular faces with dimensions 3 cm x 4 cm and 3 cm x 5 cm.
3. One square face with side length 3 cm.
First, calculate the areas of each face:
1. Triangular faces: 2 * (1/2 * base * height) = 2 * (1/2 * 4 cm * 4 cm) = 16 cm²
2. Rectangular faces: 2 * (3 cm * 4 cm + 3 cm * 5 cm) = 2 * (12 cm² + 15 cm²) = 54 cm²
3. Square face: (3 cm)² = 9 cm²
Now, add up the areas of all faces to find the total surface area of the triangular prism:
16 cm² (triangular faces) + 54 cm² (rectangular faces) + 9 cm² (square face) = 79 cm²
Therefore, the surface area of the shown net for the triangular prism is 79 cm². Thank you for your patience.
The net of the triangular prism consists of 5 faces:
1. Two congruent triangular faces with base 4 cm and height 4 cm.
2. Two rectangular faces with dimensions 3 cm x 4 cm and 3 cm x 5 cm.
3. One square face with side length 3 cm.
First, calculate the areas of each face:
1. Triangular faces: 2 * (1/2 * base * height) = 2 * (1/2 * 4 cm * 4 cm) = 16 cm²
2. Rectangular faces: 2 * (3 cm * 4 cm + 3 cm * 5 cm) = 2 * (12 cm² + 15 cm²) = 54 cm²
3. Square face: (3 cm)² = 9 cm²
Now, add up the areas of all faces to find the total surface area of the triangular prism:
16 cm² (triangular faces) + 54 cm² (rectangular faces) + 9 cm² (square face) = 79 cm²
Therefore, the surface area of the shown net for the triangular prism is 79 cm². Thank you for your patience.