Math Problem Statement
Solution
This image contains a math problem related to surface area calculations of prisms. I'll extract the two main shapes from the image and walk through their solution steps.
Shape (a) - Trapezoidal Prism:
We need to calculate:
- Base area (G): The base appears to be a trapezoid, so we use the trapezoid area formula where and .
- Lateral surface area (M): The lateral surface area , where is the perimeter of the trapezoid, and is the height of the prism.
Shape (b) - Rectangular Prism:
We calculate:
- Base area (G): The base is a rectangle, so we use , where .
- Lateral surface area (M): Again, , where is the perimeter of the base and .
I will now calculate these values for both prisms.Here are the results for both prisms:
Shape (a) - Trapezoidal Prism:
- Base area (G) = 39 cm²
- Lateral surface area (M) = 225.6 cm²
Shape (b) - Rectangular Prism:
- Base area (G) = 24 cm²
- Lateral surface area (M) = 104 cm²
Would you like me to proceed with calculating the total surface areas or any other details? Let me know if you have questions!
Here are 5 related questions to deepen your understanding:
- How do you calculate the total surface area of these prisms?
- How does the shape of the base affect the surface area?
- What formula would you use if the base of a prism was a triangle?
- How would increasing the height of the prism affect the lateral surface area?
- Can you find the volume of each prism using the base area?
Tip: Always check that the perimeter formula is adapted to the specific base shape when calculating lateral surface area.
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Math Problem Analysis
Mathematical Concepts
Surface Area
Prisms
Geometry
Formulas
Trapezoid area formula: G = (1/2) * (a + b) * h
Rectangle area formula: G = a * b
Lateral surface area formula: M = u * h_k
Total surface area formula: O = 2 * G + M
Theorems
Geometry of prisms
Suitable Grade Level
Grades 7-9