CurriculumGrade 10Mathematics

Perimeter and Area with Coordinates

Aligned to G-GPE.B.7 — Common Core State Standards for Mathematics.

What this lesson teaches

With vertices given as coordinates, use the distance formula to find each side length, then add them for perimeter. For area of a triangle or rectangle, find a base and a perpendicular height from the coordinates, or use a known formula once dimensions are computed.

Worked example

Find the perimeter of the triangle with vertices A(0,0), B(3,0), C(3,4). Side AB = 3 (horizontal). Side BC = 4 (vertical). Side CA = sqrt((3-0)^2 + (4-0)^2) = sqrt(9 + 16) = sqrt(25) = 5. Perimeter = 3 + 4 + 5 = 12 units. The right angle at B also gives area = (1/2)(3)(4) = 6 square units.

Practice questions

  1. Find the length of the segment from (1, 2) to (4, 6).
  2. Find the perimeter of the rectangle with vertices (0,0), (5,0), (5,2), (0,2).
  3. Find the area of the triangle with vertices (0,0), (6,0), (0,8).

Watch the lesson

Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

▶ Watch this lesson

En español

Perímetro y área con coordenadas

Con los vértices dados como coordenadas, usa la fórmula de distancia para hallar cada lado, luego súmalos para el perímetro. Para el área de un triángulo o rectángulo, halla una base y una altura perpendicular a partir de las coordenadas, o usa una fórmula conocida una vez calculadas las dimensiones.

Ejemplo: Halla el perímetro del triángulo con vértices A(0,0), B(3,0), C(3,4). Lado AB = 3 (horizontal). Lado BC = 4 (vertical). Lado CA = raíz((3-0)^2 + (4-0)^2) = raíz(9 + 16) = raíz(25) = 5. Perímetro = 3 + 4 + 5 = 12 unidades. El ángulo recto en B también da área = (1/2)(3)(4) = 6 unidades cuadradas.

More Expressing Geometric Properties with Equations lessons

Equation of a ParabolaG-GPE.A.2Equations of Ellipses and HyperbolasG-GPE.A.3Coordinate ProofsG-GPE.B.4Slope Criteria for Parallel and PerpendicularG-GPE.B.5Partitioning a Segment in a RatioG-GPE.B.6

Teach this lesson today

An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.

Start free — no card required