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G-GPE.7 Warmup M1-046-A06-V01

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

Find the area of a right triangle from its coordinates

Problem

Find the area of the right triangle with vertices \(A(0,~0)\), \(B(5,~0)\), and \(C(0,~6)\).

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

Start by spotting the two sides that meet at a right angle; those are already a base and its perpendicular height. Read each length from the coordinate span, then use half their product, since a right triangle occupies exactly half of the rectangle built on those legs.

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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 right triangle from its coordinates