10.5 Perimeter and Area on the Coordinate Plane p 549

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10.5 Perimeter and Area on the Coordinate Plane p 549 CCSS 7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★

Essential Question How do you find the perimeter and area of polygons in the coordinate plane?

Warm up What is the definition of perimeter? Write down the distance formula.

Explore: Finding Perimeters of Figures on the Coordinate Plane Follow these steps to find the perimeter of a pentagon with vertices A ( - 1 , 4) , B(4, 4) , C(3 , - 2 ), D(-1, -4), and E(-4, 1). Round to the nearest tenth.

A. Plot the points. Then use a straightedge to draw the pentagon that is determined by the points. B. Are there any sides for which you do not need to use the Distance Formula? Explain, and give their length(s). C. Use the Distance Formula to find the remaining side lengths. Round your answers to the nearest tenth. D. Find the sum of the side lengths.

Reflection Explain how you can find the perimeter of a rectangle to check that your answer is reasonable.

Area Formulas

Find the area: 1.

Step I: Find the coordinates of the vertices of ΔABC. Step 2: Choose a base for which you can easily find the height of the triangle. Step 3: Find the length of the base and the height using distance formula. Step 4: Find the area using the area formula.

A(-4, -2), a(-2, 2), (5, 1)

Example 2

Step 1 Find the coordinates of the vertices of DEFG. Step 2 DEFG appears to be a rectangle. Use slopes to check that adjacent sides are perpendicular or parallel. Step 3 Find the base and height of rectangle with the distance formula. Step 4. Find the area.

Assignment 1. Find the area of quadrilateral JKLM with vertices J(– 4, –2), K(2, 1), L(3, 4), M(–3, 1).

Find the perimeter of the figure with the given vertices Find the perimeter of the figure with the given vertices. Round to the nearest tenth. 2. D(0, 1), E(5, 4), and F(2, 6) 3. P(2, 5), Q(-3, 0), R(2, -5), and S(6, 0)

Find the area of the figure. 4. 5.