Lets have a brief overview of the formulae to find the perimeter and - PowerPoint PPT Presentation

D AY 117 – P ERIMETER AND AREA OF A SQUARE AND A RECTANGLE ON XY - PLANE

I NTRODUCTION We have learned how to find both the perimeter and area of squares and rectangles in our elementary grades by applying the appropriate formulae when given their dimensions. In coordinate geometry, we can also calculate the area of a square and a rectangle on the 𝑌𝑍 - plane by applying the appropriate formula and using coordinates and applying the distance formula to find the dimensions. In this lesson, we are going to learn how to find the perimeter and area of a square and a rectangle on the 𝑌𝑍 - plane.

V OCABULARY 1. Perimeter The distance around a given plane figure. 2. Area The amount of space bounded by a plane figure.

Lets have a brief overview of the formulae to find the perimeter and area of both a square and a rectangle. Perimeter of a square = 4 × length of any side Perimeter of a rectangle = 2 length + breadth Area of a square = length of any side 2 Perimeter of a rectangle = length × breadth

F INDING THE AREA AND PERIMETER OF A SQUARE ON THE XY - PLANE In order to find both the area and perimeter of a square on the xy- plane, we only need to find the length of any side of the square using the distance formula.

Example 1 Find the area and perimeter of a square whose vertices are: 𝐻 0, −3 , 𝐵 4, 0 , 𝑈 1, 4 and 𝑁 −3, 1 Solution A square has all its four sides congruent. We, therefore, need to find the length of only one side using, the distance formula. We find the length of side AG. 4 − 0 2 + 0 + 3 2 = AG = 25 = 5 units

We then apply the appropriate formula to calculate the perimeter and area of square: The perimeter of square = 4 × 5 = 20 units The area of square = 5 × 5 = 25 square units

F INDING THE AREA AND PERIMETER OF A RECTANGLE ON THE XY - PLANE In order to find both the area and perimeter of a rectangle on the xy- plane, we need to calculate the lengths of any two adjacent sides of the rectangle using the distance formula. The longer side will be the length and the shorter side will be the width( breadth). We then apply the appropriate formula to find both the area and the perimeter of the rectangle.

Example 2 Find the perimeter and area of a rectangle with vertices 𝑅 −1, 3 , 𝑆 2, 0 , 𝑇 4, 2 and 𝑈 1, 5 . Solution We find the length of two adjacent sides. −1 − 2 2 + 3 − 0 2 = 𝑅𝑆 = 18 = 3 2 4 − 2 2 + 2 − 0 2 = 𝑆𝑇 = 8 = 2 2 The length is 3 2 and the width is 2 2 Perimeter = 2 3 2 + 2 2 = 2 × 5 2 = 10 2 = 14.14 units Area = 18 × 8 = 144 = 12 square units

HOMEWORK A Rectangle has the following vertices: 𝑁 −4, 0 , 𝐵 −3, −3 , 𝐸 3, −1 and 𝐹 2, 2 Determine its perimeter and area.

A NSWERS TO HOMEWORK Perimeter = 18.97 units Area = 20 square units

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