Math Problem Statement

The front and side elevations of a solid shape are shown on the grid. Draw a plan view of the solid shape.

Solution

To draw the plan view of the solid shape, we will analyze the given side and front elevations.

Step-by-step approach:

  1. Understanding the side elevation:

    • The side elevation suggests that the shape has three distinct heights.
    • The base layer is 2 squares wide, the middle layer is 1 square wide, and the top layer is 1 square wide, each being stacked on top of each other.
  2. Understanding the front elevation:

    • The front elevation shows that the shape consists of two sections stacked vertically, with a width of 2 squares. The lower section is 2 squares high and 2 squares wide, and the upper section is 1 square high and 2 squares wide.

Drawing the plan view:

The plan view is a bird’s-eye view (from the top) of the shape, so it shows the footprint of the object.

  • The base layer is 2 squares wide and 2 squares deep.
  • The middle layer is 1 square wide and 1 square deep, starting from the top left.
  • The top layer is 1 square wide and 1 square deep, aligned with the middle layer.

Sketch:

  • The bottom layer will be a 2×2 square.
  • The top layer will be a 1×1 square positioned at the top left of the base square.

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Questions to deepen understanding:

  1. What is the difference between front elevation, side elevation, and plan view?
  2. How do you use the grid to determine the plan view of a solid?
  3. How does stacking affect the appearance of different views of a 3D shape?
  4. Can you identify the total height of the solid based on both elevations?
  5. How would the plan view change if a section of the object was missing?

Tip: When working on 3D views, always align the sections carefully to avoid misinterpretations of depth and height.

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Math Problem Analysis

Mathematical Concepts

Geometry
3D shapes
Plan and Elevation Views

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9