To find the missing length \(l\) of the triangular prism, we need to calculate the surface area of the entire prism and then solve for \(l\).
The surface area of a triangular prism can be calculated using the formula:
\[
SA = 2B + PH
\]
where \(B\) is the area of the front triangular face and \(PH\) is the sum of the areas of the two rectangular faces.
1. Calculate the area of the front triangular face:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
A_{\text{triangle}} = \frac{1}{2} \times 8 \times 6
\]
\[
A_{\text{triangle}} = 24 \, \text{cm}^2
\]
2. Calculate the perimeter of the front triangle:
\[
\text{Perimeter} = 10 + 10 + 8 = 28 \, \text{cm}
\]
3. Calculate the height of the rectangular faces:
\[
\text{Height of rectangular face} = 6 \, \text{cm}
\]
4. Substitute the values into the formula for the total surface area:
\[
524 = 2(24) + 28(6) + 8l
\]
\[
524 = 48 + 168 + 8l
\]
\[
524 = 216 + 8l
\]
\[
8l = 308
\]
\[
l = 38.5 \, \text{cm}
\]
Therefore, the missing length \(l\) of the triangular prism is 38.5 centimeters.
.
An illustration shows 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 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.
What is the missing length l
of the triangular prism if the surface area is 524 square centimeters?
3 answers
incorrect
I apologize for the mistake. Let's correct the calculation:
1. Calculate the area of the front triangular face:
Area\_triangle = 1/2 \* base \* height
Area\_triangle = 1/2 \* 8 \* 6
Area\_triangle = 24 square centimeters
2. Calculate the perimeter of the front triangle:
Perimeter = 10 + 10 + 8 = 28 cm
3. Calculate the area of the two rectangular faces:
Area\_rectangles = 2 \* base \* height
Area\_rectangles = 2 \* 8 \* 6
Area\_rectangles = 96 square centimeters
4. Calculate the total surface area of the triangular prism:
Total\_SA = 2 \* Area\_triangle + Perimeter \* height + 2 \* Area\_rectangles
Total\_SA = 2 \* 24 + 28 \* 6 + 96
Total\_SA = 48 + 168 + 96
Total\_SA = 312 cm\^2
Now, we know that the total surface area of the triangular prism is 524 cm\^2. Let's solve for the missing length \(l\):
524 = 2 \* 24 + 28 \* 6 + 2 \* 96 + 8l
524 = 48 + 168 + 192 + 8l
524 = 408 + 8l
8l = 116
l = 14.5 cm
Therefore, the missing length \(l\) of the triangular prism is 14.5 centimeters. Thank you for your patience.
1. Calculate the area of the front triangular face:
Area\_triangle = 1/2 \* base \* height
Area\_triangle = 1/2 \* 8 \* 6
Area\_triangle = 24 square centimeters
2. Calculate the perimeter of the front triangle:
Perimeter = 10 + 10 + 8 = 28 cm
3. Calculate the area of the two rectangular faces:
Area\_rectangles = 2 \* base \* height
Area\_rectangles = 2 \* 8 \* 6
Area\_rectangles = 96 square centimeters
4. Calculate the total surface area of the triangular prism:
Total\_SA = 2 \* Area\_triangle + Perimeter \* height + 2 \* Area\_rectangles
Total\_SA = 2 \* 24 + 28 \* 6 + 96
Total\_SA = 48 + 168 + 96
Total\_SA = 312 cm\^2
Now, we know that the total surface area of the triangular prism is 524 cm\^2. Let's solve for the missing length \(l\):
524 = 2 \* 24 + 28 \* 6 + 2 \* 96 + 8l
524 = 48 + 168 + 192 + 8l
524 = 408 + 8l
8l = 116
l = 14.5 cm
Therefore, the missing length \(l\) of the triangular prism is 14.5 centimeters. Thank you for your patience.