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Find the perimeters and areas of figures in a coordinate plane.

Learn how to find perimeters and areas of figures in a coordinate plane with step-by-step examples. Understand properties of polygons and use formulas to calculate perimeters and areas efficiently.

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Find the perimeters and areas of figures in a coordinate plane.

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  1. Objective Find the perimeters and areas of figures in a coordinate plane.

  2. Check It Out! Example 2 Draw and classify the polygon with vertices H(–3, 4), J(2, 6), K(2, 1), and L(–3, –1). Find the perimeter and area of the polygon. Step 1 Draw the polygon.

  3. Check It Out! Example 2 Continued Step 2 HJKL appears to be a parallelogram. To verify this, use slopes to show that opposite sides are parallel.

  4. are vertical lines. Check It Out! Example 2 Continued The opposite sides are parallel, so HJKL is a parallelogram.

  5. Check It Out! Example 2 Continued Step 3 Since HJKL is a parallelogram, HJ = KL, and JK = LH. Use the Distance Formula to find each side length. perimeter of EFGH:

  6. Check It Out! Example 2 Continued To find the area of HJKL, draw a line to divide HJKL into two triangles. The base and height of each triangle is 3. The area of each triangle is The area of HJKL is 2(12.5) = 25 units2.

  7. Example 3: Finding Areas in the Coordinate Plane by Subtracting Find the area of the polygon with vertices A(–4, 1), B(2, 4), C(4, 1), and D(–2, –2). Draw the polygon and close it in a rectangle. Area of rectangle: A = bh = 8(6)= 48 units2.

  8. Example 3 Continued Area of triangles: The area of the polygon is 48 – 9 – 3 – 9 – 3 = 24 units2.

  9. Check It Out! Example 3 Find the area of the polygon with vertices K(–2, 4), L(6, –2), M(4, –4), and N(–6, –2). Draw the polygon and close it in a rectangle. Area of rectangle: A = bh = 12(8)= 96 units2.

  10. Check It Out! Example 3 Continued Area of triangles: b a d c The area of the polygon is 96 – 12 – 24 – 2 – 10 = 48 units2.

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