To find the surface area of the triangular prism display showcase, we need to calculate the surface areas of each of the three rectangular faces and two triangular faces.
First, we calculate the surface area of the triangular faces:
Area of triangle 1 = (1/2) * s¹ * h = (1/2) * 10 * 9 = 45 square inches
Area of triangle 2 = (1/2) * s² * h = (1/2) * 12 * 9 = 54 square inches
Area of triangle 3 = (1/2) * s³ * h = (1/2) * 17 * 9 = 76.5 square inches
Now, we calculate the surface area of the rectangular faces:
Area of rectangular face 1 = b * h = 17 * 9 = 153 square inches
Area of rectangular face 2 = l * h = 10 * 9 = 90 square inches
Finally, we sum the areas of all five faces:
Total surface area = 45 + 54 + 76.5 + 153 + 90 = 418.5 square inches
Therefore, the surface area of Christian's display showcase is 418.5 square inches.
Christian collects model cars and planes. he has a display showcase of those 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, s¹=10 inches, s²=12 inches, s³=17 and l=10 inches.
3 answers
wrong answer.
I apologize for the mistake. Let's correct it.
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2 * triangle areas + rectangle areas
First, let's calculate the areas of the two triangular faces:
Area of triangle 1 = (1/2) * s¹ * h = (1/2) * 10 * 9 = 45 square inches
Area of triangle 2 = (1/2) * s² * h = (1/2) * 12 * 9 = 54 square inches
Now, let's calculate the areas of the three rectangular faces:
Area of rectangular face 1 = b * h = 17 * 9 = 153 square inches
Area of rectangular face 2 = l * h = 10 * 9 = 90 square inches
Area of rectangular face 3 = l * s³ = 10 * 17 = 170 square inches
Now, we can find the total surface area:
Surface Area = 2 * (45 + 54) + 153 + 90 + 170 = 2 * 99 + 153 + 90 + 170 = 198 + 153 + 90 + 170 = 611 square inches
Therefore, the surface area of Christian's display showcase is 611 square inches. Thank you for your patience.
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2 * triangle areas + rectangle areas
First, let's calculate the areas of the two triangular faces:
Area of triangle 1 = (1/2) * s¹ * h = (1/2) * 10 * 9 = 45 square inches
Area of triangle 2 = (1/2) * s² * h = (1/2) * 12 * 9 = 54 square inches
Now, let's calculate the areas of the three rectangular faces:
Area of rectangular face 1 = b * h = 17 * 9 = 153 square inches
Area of rectangular face 2 = l * h = 10 * 9 = 90 square inches
Area of rectangular face 3 = l * s³ = 10 * 17 = 170 square inches
Now, we can find the total surface area:
Surface Area = 2 * (45 + 54) + 153 + 90 + 170 = 2 * 99 + 153 + 90 + 170 = 198 + 153 + 90 + 170 = 611 square inches
Therefore, the surface area of Christian's display showcase is 611 square inches. Thank you for your patience.