Area and perimeter in the coordinate plane I

Key Notes :

Area of a square:
Area=s2

Learn with an example

✈️ What is the perimeter of square STUV?

Area= _____ square units

  • Look at the graph of square STUV to find the coordinates of the vertices.
  • To find the area of square STUV, first calculate its side length. Then, plug this value into the formula for the area of a square.
  • Step 1: Find the side length.
  • All sides of a square have the same length. So, pick any of the four sides.
  • The distance between the vertices S(1,–9) and T(1,1) is the side length of the square.
  • Since S(1,–9) and T(1,1) have the same x-coordinate, ST is the absolute value of the difference in the y-coordinates, which is |–9–1|=10. So, the length is 10.
  • Step 2: Find the area.
  • Now, plug in the value for the side length into the formula for the area of a square.
  • Area of a square
  • = s2
  • = 102 Plug in s=10
  • = 100 Square
  • So, the area of square STUV is 100 square units.

✈️ What is the perimeter of square EFGH?

Perimeter= _____ units

  • Look at the graph of square EFGH to find the coordinates of the vertices.
  • To find the perimeter of square EFGH, first calculate its side length. Then, plug this value into the formula for the perimeter of a square.
  • Step 1: Find the side length.
  • All sides of a square have the same length. So, pick any of the four sides.
  • The distance between the vertices E(10,– 4) and F(–2,–4) is the side length of the square.
  • Since E(10,–4) and F(–2,–4) have the same y-coordinate, EF is the absolute value of the difference in the x-coordinates, which is |10– –2|=12. So, the length is 12.
  • Step 2: Find the perimeter.
  • Now, plug in the value for the side length into the formula for the perimeter of a square.
  • Perimeter of a square
  • = 4s
  • = 4(12) Plug in s=12
  • = 48 Multiply
  • So, the perimeter of square EFGH is 48 units.

✈️ What is the perimeter of square BCDE?

Perimeter= ________ units

  • Look at the graph of square BCDE to find the coordinates of the vertices.
  • To find the perimeter of square BCDE, first calculate its side length. Then, plug this value into the formula for the perimeter of a square.
  • Step 1: Find the side length.
  • All sides of a square have the same length. So, pick any of the four sides.
  • The distance between the vertices B(6,3) and C(3,3) is the side length of the square.
  • Since B(6,3) and C(3,3) have the same y-coordinate, BC is the absolute value of the difference in the x-coordinates, which is |6–3|=3. So, the length is 3.
  • Step 2: Find the perimeter.
  • Now, plug in the value for the side length into the formula for the perimeter of a square.
  • Perimeter of a square
  • = 4s
  • = 4(3) Plug in s=3
  • = 12 Multiply
  • So, the perimeter of square BCDE is 12 units.

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