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Geometry - Perimeter and Area - Page 1

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Geometry - Perimeter and Area

This document provides study materials related to Geometry - Perimeter and Area. It may include explanations, summarized notes, examples, or practice questions designed to help students understand key concepts and review important topics covered in their coursework.

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Geometry - Perimeter and Area - Page 1 preview imageStudy GuideGeometry–Perimeter and Area1. Parallelograms1.1Base and HeightIn a parallelogram:•Abaseis any side you choose.•Theheight (h)is the perpendicular distance from that base to the opposite side.Important:The height must form aright angle (90°)with the base.In the diagram:•One base is labeledb.•The non-base sides are labeleda.•The perpendicular segment is theheight (h).Figure 1
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Geometry - Perimeter and Area - Page 2 preview imageStudy Guide1.2Finding the PerimeterThe perimeter is the total distance around the shape.Since opposite sides of a parallelogram are equal:•Two sides are lengtha•Two sides are lengthbSo the perimeter formula is:You may also see it written as:Both formulas mean the same thing.1.3Finding the AreaTo find the area of a parallelogram, think of it like a rectangle.If you rearrange parts of the parallelogram, it can form a rectangle with the same base and height.That’s why the area formula is:Where:•bis the base•his the heightThe area is always the base multiplied by its corresponding height.
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Geometry - Perimeter and Area - Page 3 preview imageStudy GuideExample 1:SolveFind theperimeterandareaof the parallelogram shown.Given:•Base = 14 cm•Side = 10 cm•Height = 8 cmFigure 2Step 1: Find the PerimeterUse the formula:
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Geometry - Perimeter and Area - Page 4 preview imageStudy GuideStep 2: Find the AreaUse the formula:Summary•Opposite sides of a parallelogram are equal.•Perimeter formula:P = 2(a + b)•Area formula:A = bh•The height must be perpendicular to the base.•You can choose any side as the base, but use the matching height.2. TrianglesLet’s look at how triangles are connected to parallelograms.Imagine triangleABD.If we draw:•A line throughBparallel toAD, and•A line throughDparallel toAB,we form aparallelogram.The diagonalBDdivides that parallelogram intotwo congruent triangles.That means:The area of triangle ABD is exactlyhalfthe area of the parallelogram.
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Geometry - Perimeter and Area - Page 5 preview imageStudy GuideFigure 12.1Finding the Area of a TriangleWe know:Since a triangle is half of that parallelogram:Where:•bis the base•his the height (perpendicular to the base)2.2Finding the Perimeter of a TriangleThe perimeter of a triangle is simple.Just add all three sides:
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Geometry - Perimeter and Area - Page 6 preview imageStudy GuideExample 1:SolveFind theperimeterandareaof each triangle in Figures (a), (b), and (c).Figure 2(a)PerimeterArea(b)PerimeterArea
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Geometry - Perimeter and Area - Page 7 preview imageStudy Guide(c)PerimeterAreaExample 2:SolveA triangle has:•Area = 64 cm²•Height = 16 cmFind the base.Step 1: Use the Area FormulaStep 2: Multiply Both Sides by 2Step 3: Solve for bThe base of the triangle is:
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Geometry - Perimeter and Area - Page 8 preview imageStudy GuideSummary•A triangle’s area is half the area of its associated parallelogram.•Area formula:•Perimeter formula:•The height must be perpendicular to the base.3. TrapezoidsTrapezoids are one of the most common quadrilaterals in real life.In fact, many old railroad bridges and wooden trestles were built in trapezoidal shapes because theyare strong and stable.Let’s explore how to find theperimeterandareaof a trapezoid.3.1Parts of a TrapezoidIn trapezoidQRSV:•(b1)and(b2)are thebases(the parallel sides).•(a)and(c)are thelegs(the nonparallel sides).•(h)is theheight, drawn perpendicular to the bases.Theperimeteris simply the sum of all four sides.
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Geometry - Perimeter and Area - Page 9 preview imageStudy GuideFigure 13.2Finding the Area of a TrapezoidHere’s a helpful idea:If you place an identical trapezoid upside down next to the original one, together they form aparallelogram.The base of that parallelogram becomes:And the height remains:So the area of the parallelogram is:But one trapezoid is onlyhalfof that parallelogram.So the area formula for a trapezoid is:
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Geometry - Perimeter and Area - Page 10 preview imageStudy GuideExample 1:SolveFind theperimeterandareaof the trapezoid shown.Given:•Left leg = 17 cm•Top base = 7 cm•Right leg = 10 cm•Bottom base = 28 cm•Height = 8 cmFigure 2Step 1: Find the PerimeterUse the perimeter formula:Step 2: Find the AreaUse the area formula:
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Document Details

University
Texas A&M University
Course
Geometry
Subject
Mathematics

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