Problem preview

G-SRT.9 Warmup M3-044-A06-V01

Derive the triangle area formula A=1/2ab sin(C) using an auxiliary altitude.

Find a triangle’s area from two sides and the included angle by writing the altitude as side × sine

Problem

The triangle shown has base \(12\) and perpendicular height \(5\). State the most direct area formula for the given measurements.

Triangle with a horizontal base labeled 12 and its perpendicular altitude labeled 5.

Big Picture

What this problem is really about

Inventory the measurements before reaching for a formula. When a base and its corresponding perpendicular height are already supplied, one-half base times height uses the data directly; no trigonometric conversion or additional side is needed. The factor of one-half distinguishes the triangle from the rectangle or parallelogram with the same base and height.

Answer choices

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Preview only

Use A = 1/2bh

Use A = 1/2ab sin(C)

Use Heron’s formula

Use A = bh

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Curriculum context

Course: Math III
Standard: G-SRT.9
Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Objective: Derive the triangle area formula A=1/2ab sin(C) using an auxiliary altitude.
Problem type: Find a triangle’s area from two sides and the included angle by writing the altitude as side × sine