Use the image to answer the question.
A triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side of the triangle measures 8 centimeters. The left side meets the base to form a right angle. The base of the triangle measures 6 centimeters. The hypotenuse side of the triangle measures 10 centimeters. The width of the rectangular face measures 9 centimeters.
What is the surface area of the triangular prism?
To find the surface area of a triangular prism, we need to calculate the areas of all the individual faces and add them together.
First, let's calculate the area of the front triangular face:
Area = 1/2 * base * height
Area = 1/2 * 6 cm * 8 cm
Area = 24 cm^2
Next, let's calculate the area of the rectangular face:
Area = length * width
Area = 9 cm * 6 cm
Area = 54 cm^2
Now, let's calculate the area of the two side triangular faces:
Since the two side triangular faces are congruent and right triangles, we can use the Pythagorean theorem to find the height of the triangle.
a^2 + b^2 = c^2
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
c = √100
c = 10
Now, let's calculate the area of one side triangle:
Area = 1/2 * base * height
Area = 1/2 * 6 cm * 10 cm
Area = 30 cm^2
There are two side triangular faces, so the total area of both side triangular faces is 30 cm^2 + 30 cm^2 = 60 cm^2.
Now, we can add up all the areas to find the total surface area of the triangular prism:
Total surface area = front triangular face area + rectangular face area + 2(side triangular faces area)
Total surface area = 24 cm^2 + 54 cm^2 + 60 cm^2
Total surface area = 138 cm^2
Therefore, the surface area of the triangular prism is 138 square centimeters.
your wrong
I apologize for the error in my previous response. Let's correct the calculation:
Front triangular face surface area = 1/2 * base * height
Front triangular face surface area = 1/2 * 6cm * 8cm
Front triangular face surface area = 24 square cm
Rectangular face surface area = length * width
Rectangular face surface area = 9cm * 6cm
Rectangular face surface area = 54 square cm
Side triangular faces are right angled triangles. The hypotenuse is the height of the rectangle, so the length of the two sides of the triangle are 6cm and 9cm, with a hypotenuse of 10cm. Using Pythagorean theorem, the height of the triangle can be calculated as:
height = sqrt(10^2 - 6^2)
height = sqrt(100 - 36)
height = sqrt(64)
height = 8cm
Area of one side triangular face = 1/2 * base * height
Area of one side triangular face = 1/2 * 6cm * 8cm
Area of one side triangular face = 24 square cm
Total surface area = 2(side triangular face area) + front triangular face area + rectangular face area
Total surface area = 2(24 square cm) + 24 square cm + 54 square cm
Total surface area = 48 square cm + 24 square cm + 54 square cm
Total surface area = 126 square cm
Therefore, the correct surface area of the triangular prism is 126 square centimeters. Thank you for pointing out the mistake!