A small staircase is made so that the horizontal piece of...

Name: Problem 5, Chapter 8: Grade 7 Mathematics: Open Up Resources, Common Core State Standards Edition
Uploaded: 2022-01-24T19:59:41-08:00
Duration: 3 min 42 s
Channel: Allison Knapp
Description: A small staircase is made so that the horizontal piece of each step is 10 inches long and 25 inches wide. Each step is 5 inches above the previous one. What is the surface area of this staircase?

A small staircase is made so that the horizontal piece of each step is 10 inches long and 25 inches wide. Each step is 5 inches above the previous one. What is the surface area of this staircase?

Key Concepts

Decomposition of Complex Shapes

Decomposition is the process of analyzing a complex structure by dividing it into simpler, more manageable shapes. This concept is crucial when calculating the surface area of objects that do not have a standard geometric form, as it allows the use of basic area formulas while systematically accounting for every visible face of the structure.

Overlapping and Hidden Surfaces

In many three-dimensional objects, some surfaces are partially or completely hidden behind others, or they overlap with adjacent components. Understanding which surfaces are exposed and which are not is essential in ensuring that areas are neither double-counted nor omitted when computing the total surface area.

Composite Figures

Composite figures are shapes that can be divided into simpler geometric components, such as rectangles or triangles. Breaking down a complex structure into these basic components allows for easier calculation of total area by summing the areas of each piece, taking into consideration their arrangement and any shared boundaries.

Surface Area

Surface area is a measure of the total area that the surface of a three-dimensional object occupies. In problems involving complex shapes, calculating the surface area often requires identifying and summing the areas of all individual external faces while carefully accounting for overlaps and hidden surfaces.

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