University:
High School
Course:
High School Geometry
Academic year:

2019
Views:

373

Pages:

4
Author:

nekomiyunz

Perimeter and Area in the Coordinate Plane List of terms you should recognize in a picture and apply formula (as covered in class) polygon 1 closed, straight-sided shape. n-gon n = any number of sides I want n = any name for any polygon not on the chart side Segment that makes up the polygon convex polygons that have points going outwards concave polygons that have points going inwards vertex intersection of two sides Extra Practice In Exercises 1-4, classify the polygon by the number of sides. Tell whether it is convex or concave. 5-sides = pentagon concave 8-sides = octagon convex 8-sides = octagon concave 12-sided = dodecagon convex Extra Practice In Exercises 5-8, find the perimeter and area of the polygon with the given vertices. 5. X(2,4), Y(0,2), Z(2,-2) coordinate plane with points X(2,4), Y(0,2), and Z(2,2) forming a right triangle Area = 1/2 * b * h = 1/2 * 2 * 6 = 6 Perimeter = XY + XZ + YZ = √[(0-2)² + (2-4)²] + 6 + 2 = √[(-2)² + (-2)²] + 8 = √[4 + 4] + 8 = √8 + 8 = 2√2 + 8 = 10.83 + 8 P = 18.83 6. P(1,3), Q(1,1), R(-4,2) coordinate plane with points P(1,3), Q(1,1), and R(4,2) forming a triangle Area = 1/2 * b * h = 1/2 * 5 * 2 = 5 Perimeter = PQ + QR + RP = 2 + √[1² + 5²] + √[1² + 5²] = 2 + √[1 + 25] + √[1 + 25] = 2 + √26 + √26 = 2 + 2√26 7. J(4,1), K(-2,4), L(6,1), M(6,1) coordinate plane with points J(4,1), K(2,4), L(6,1), and M(6,1) forming a trapezoid Area = b * h = 10 * 3 = 30 Perimeter = JM + ML + KL + JK = 10 + 3 + 10 + 3 = 12 + 13 = 26 8. D(5,-3), E(5,-6), F(2,-6), G(2,-3) coordinate plane with points D(5,3), E(5,6), F(2,6), and G(2,3) forming a rectangle Area = b * h = 3 * 3 = 9 Perimeter = 3 + 3 + 3 + 3 = 12 Extra Practice In Exercises 9-14, use the diagram. 9. Find the perimeter of ∆ABD. Perimeter = AB + BD + DA = 5 + 6 + √(5² + 6²) = 11 + √(25 + 36) = 11 + √61 10. Find the perimeter of ABCD. Perimeter = BD + BC + CD = 6 + √(4² + 3²) + √(4² + 3²) = 6 + √(16 + 9) + √(16 + 9) = 6 + √25 + √25 = 6 + 5 + 5 = 16 *Always reduce when it's a perfect square 11. Find the perimeter of quadrilateral ABCD. Perimeter = AD + AB + BC + CD = 6 + 5 + 5 + 5 = 16 + 15 = 31 *We already know these from the earlier problems