CCSS.Math.Content.HSG-GPE.B.7
The Standard
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use coordinates to find side lengths, including diagonal lengths with the distance formula. They add side lengths for perimeter and calculate areas of triangles and rectangles.
What Mastery Looks Like
- Students correctly find horizontal, vertical, and diagonal side lengths from coordinates. They sum lengths for perimeter, calculate area, and use linear or square units correctly.
Common Misconceptions
- Students may add coordinate values instead of finding side lengths. They also confuse perimeter with area, omit diagonal sides, or give square units for perimeter.
How to Assess It
- Exit ticket: Triangle A(0,0), B(6,0), and C(6,8) has what perimeter and area? Show each side length and label units.
Lesson moves
Ways to Teach It
On graph paper, students plot four given vertices, connect them, measure each side, then calculate the polygon’s perimeter and area.
Ask students to explain why subtracting x-coordinates alone cannot find every side length in a coordinate polygon.
Play a matching game with coordinate cards, diagrams, side-length calculations, and correct perimeter or area values.
Give students a coordinate map of a garden plot and ask them to calculate fencing needed and planting area.
Free download
Printable HSG-GPE.B.7 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-GPE.B.7, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.G.B.8
Finding side lengths between coordinate points is needed to compute polygon perimeters and many triangle or rectangle areas.
- CCSS.Math.Content.7.G.B.6
Area formulas for triangles and rectangles carry over when coordinate side lengths are found with the distance formula.
- CCSS.Math.Content.7.NS.A.3
Computing side lengths, perimeters, and areas from coordinates requires subtracting, multiplying, and adding rational number coordinate values accurately.
What This Unlocks
Mastery here sets students up for these next.
Keep exploring
Related Standards
- CCSS.Math.Content.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other sha...
- CCSS.Math.Content.3.MD.D.8
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side len...
- CCSS.Math.Content.6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordi...
- CCSS.Math.Content.4.MD.A.3
Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
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