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G-GPE.7 Warmup M1-046-A05-V01

Use coordinate methods to compute polygon perimeters and areas of triangles/rectangles.

Find the area of a triangle on the coordinate plane when one base is horizontal or vertical

Problem

Find the area of the triangle described here: base from \((0,0)\) to \((6,0)\), third vertex \((2,4)\).

Actual coordinate polygon or dimensioned source figure containing only information supplied in the prompt. Open full size
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What this problem is really about

Use the horizontal side as the base, then measure height perpendicular to its line rather than along a slanted side. Because the base lies on a constant y-value, the height is the absolute vertical difference to the third vertex; its x-coordinate only locates the foot of that perpendicular.

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Four variants of this problem type
Curriculum context
Course
Math I
Standard
G-GPE.7
Category
Geometry
Domain
Expressing Geometric Properties with Equations
Objective
Use coordinate methods to compute polygon perimeters and areas of triangles/rectangles.
Problem type
Find the area of a triangle on the coordinate plane when one base is horizontal or vertical