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Perimeter and Area in the Coordinate Plane

In this topic, we learn to find the perimeter and areas of figures in a coordinate plane.

Topic: Estimating Areas of Irregular Shapes in the Coordinate Plane

  • We can estimate the area of irregular shapes by drawing composite figures that approximate the irregular shapes and by using area formulas

  • Another method of estimating area is to use a grid and count the squares on the grid

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Topic: Perimeter and Area in the Coordinate Plane

  • The distance from (x1, y1) to (x2, y2) in a coordinate plane is d = √((x2 - x1)2 + (y2 - y1)2) and the slope of the line containing the points is m = (y2 - y1)/(x2 - x1)

  • The perimeter of a figure is the sum of its side lengths

  • The area of a triangle with base b and height h is A = (1/2)bh

  • The area of a rectangle with base b and height h is A = bh

  • The area of a trapezoid with bases b1­ and b2 and height h is A = (1/2)(b1 + b2)h

Topic: Find Areas in the Coordinate Plane by Subtracting

  • To find the area of a polygon in the coordinate plane, Draw the polygon and enclose it in a rectangle

  • The area of a rectangle with base b and height h is A = bh

  • The area of a triangle with base b and height h is A = (1/2)bh

  • The area of a trapezoid with bases b1­ and b2 and height h is A = (1/2)(b1 + b2)h

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Topic: Problem Solving Applications

  • If the corresponding areas are the same, then both figures have the same area by the Area Addition Postulate. To explain why the area appears to increase, consider the assumptions being made about the figure

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