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G-GPE.7 Warmup M1-046-A07-V01

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

Find the area of a polygon by decomposing it into rectangles and triangles

Problem

Find the area of this polygon by decomposing it: an L-shape made from a \(6~by~5\) rectangle with a \(2~by~3\) corner removed.

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

Treat the L-shape as a complete outer rectangle with one rectangular corner missing. Find those two areas from their side lengths and subtract the missing piece, checking that the removed region sits inside the outer boundary and is counted only once.

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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 polygon by decomposing it into rectangles and triangles