Derive triangle area formula

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Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

HSG.SRT.D.9

**HSG.SRT.D.9**: (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

HSG.SRT.D.9: (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

What you'll learn

Derive the formula A = (1/2)ab sin(C) for the area of a triangle by drawing an auxiliary altitude from a vertex perpendicular to the opposite side
Explain why the formula works for acute, right, and obtuse triangles
Apply the formula to find the area of a triangle given two sides and the included angle
Recognize when to use A = (1/2)ab sin(C) versus the base-height formula
Interpret the role of sin(C) geometrically - how the included angle controls area for fixed side lengths
Use the formula to solve real-world problems involving triangular regions

Review first: