MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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13.5 Areas

Focus on area under constant graph and triangle under a line.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Estimating area with rectanglesWorked steps · five questions02Area as a limitWorked steps · five questions
Lesson brief and rules

13.5 Areas

For a constant height hh over width ww, area under the graph is hw.

Worked example 11
01 / Find the area under y=3y=3 from x=0x=0 to x=4x=4.
02 / Rectangle height 33 times width 44 gives 1212.
03 / Answer: 1212
Worked example 2 · Triangle under a line

Find area under y=xy=x on [0,4][0,4].

The region is a right triangle with base and height 44. Answer: 162\dfrac{16}{2}

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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