12-36th grade math

Area of Triangles

Objective

• To find the area of triangles

• Why? To know how to use formulas and evaluate variable expressions using the order of operations. To further your knowledge of geometry and measurement.

California State Standards AF 3.1: Use variables in expressions describing geometric quantities

… (e.g., A = ½ bh, …- the formula for … the area of triangles …)

AF 3.2: Express in symbolic form simple relationships arising from geometry.

MR 1.1: Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, … and observing patterns.

MR 1.3: Determine when and how to break a problem into simpler parts.

MR 2.5: Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work

MR 3.2: Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

Vocabulary• Triangles– ½ of a quadrilateral• Parallelogram = b x h• Triangle = ½ b x h

How to Solve Area of Triangles1)Observe or draw the

triangle figure. Be sure all measurements are in equal labels.

2) Write out the formula: ½ x (l x w) or ½ (b x h)

3) ½ either the l or the w. Or multiply l and w and then ½ .

4) Check work and add label² to answer.

Find the area of the parallelogram. Base = 30 yd, Height = 20 yd

A = 30 x 20A = 600 yd²

Find the area of the triangle.You can split the parallelogram into 2

triangles.

A = ½ (30 x 20) or 30 x (1/2 x 20)= ½ x 600 = 30 x 10= 300 yd² = 300 yd²

Try It!

1) Triangle: 9 m, 18 m2) Triangle: 9 ft, 18 ft3) Triangle: 24 in, 6 in4) Triangle: 10 cm, 20 cm

5) Triangle: base = 1.5 m, height 850 cm

1) Triangle: 9 m, 18 m= 9 x 9 = 81 m²2) Triangle: 9 ft, 18 ft= 9 x 9 ft²= 81 m²3) Triangle: 24 in, 6 in= 12 x 6 = 72 in²4) Triangle: 10 cm, 20 cm= 10 x 10= 100 cm²5) Triangle: base = 1.5 m,

height 850 cm= 1.5 m x 4.25 m= 6.275 m²

Objective Review • To find the area of

triangles

• Why? You now know how to use formulas and evaluate variable expressions using the order of operations. You have furthered your knowledge of geometry and measurement.

• The area of a triangle is ½ times the base times the height (or ½ times the height times the base)

Independent Practice

• Complete problems 6-11

• Copy original problem first.

• Show all work!

• If time, complete Mixed Review: 12-18

• If still more time, work on Accelerated Math.