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G-GPE.7 Warmup M1-046-A08-V01

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

Use the coordinate area formula on ordered vertices

Problem

Use the shoelace formula on the ordered vertices \(A(0,0),~B(4,0),~C(0,3)\). Give the shoelace sum and the polygon's area.

Source coordinate polygon: Triangle ABC has vertices A(0,0), B(4,0), and C(0,3), listed in order; no shoelace products or area are shown. Open full size
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What this problem is really about

List the vertices in one continuous trip around the boundary and repeat the first point at the end. Form the two diagonal-product sums, take the absolute difference so orientation cannot make area negative, and divide by two; a quick sketch confirms the order before the arithmetic begins.

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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
Use the coordinate area formula on ordered vertices