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
What this standard means
Students need to use coordinate points to find side lengths, then use those lengths to calculate perimeter and area. They should know when to use counting on a grid, the distance formula, base times height, and triangle area formulas.
Mastery looks like choosing an efficient method, showing organized work, and keeping units straight. Students often get stuck finding slanted side lengths, assuming diagonal lengths from the grid, or picking the wrong base and height when a shape is tilted.
Ways to teach it
- Give pairs graph paper and coordinate cards, then have them draw a polygon and calculate its perimeter using distance formula where needed.
- Ask students: How can you find the area of a tilted rectangle without guessing its base and height from the grid?
- Use an exit ticket with one triangle and one rectangle on a coordinate plane, asking for perimeter and area with work shown.
- Have students map a simple playground on a coordinate grid, then calculate fencing length and turf area from the plotted corners.
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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.