Math Problem Statement

What is the shape of the bases? What is the name of this solid figure? What is the perimeter of the base? What is the height of the prism? Lateral area = base × height of the prism. What is the area of the base? For any prism, Surface area = base area + lateral area. For this prism, the surface area is given. For numbers 9-12, solve for the surface area of each prism.

Solution

I see you’ve uploaded a math problem that involves finding the surface area of various prisms and other solid figures. Let's break this down step by step.

Here are the first steps to approach this set of problems:

  1. Shape of the Bases and Solid Figure:

    • For each figure, we need to identify the base's shape. For example, the first figure seems to be a rectangular prism, and the base could be a rectangle.
    • Based on the shape of the base, we can identify the name of the solid figure.
  2. Perimeter of the Base:

    • If the base is a rectangle, the perimeter is calculated by the formula: P=2×(length+width)P = 2 \times (\text{length} + \text{width})
    • If it's a circle, the perimeter is the circumference: P=2πrP = 2 \pi r
  3. Height of the Prism:

    • For rectangular prisms, this would be the height of the figure itself, not the base.
  4. Lateral Area:

    • The formula for lateral area is: Lateral area=Perimeter of base×Height\text{Lateral area} = \text{Perimeter of base} \times \text{Height}
  5. Surface Area:

    • The surface area of a prism is given by the formula: Surface area=2×Base area+Lateral area\text{Surface area} = 2 \times \text{Base area} + \text{Lateral area}

For questions 9-12, we will need to apply these formulas to each specific prism.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Prisms

Formulas

Perimeter of a rectangle: P = 2 × (length + width)
Perimeter of a circle: P = 2πr
Lateral Area: Lateral area = Perimeter of base × Height
Surface Area: Surface area = 2 × Base area + Lateral area

Theorems

Surface area of a prism
Lateral area formula

Suitable Grade Level

Grades 6-9