evaluating geometric formulas core focus on introductory algebra lesson 2.3
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Evaluating Geometric Formulas
Core Focus onIntroductory Algebra
Lesson 2.3
Evaluate each expression.
1. 2x − 5 when x = 11
2. when b = 18
3. 2l + 2w when l = 5 and w = 3
16
b
Warm-Up
17
4
16
Evaluating Geometric Formulas
Use geometric formulas to find area, perimeter and volume.
Lesson 2.3
FormulaAn algebraic equation that shows the relationship among specific quantities.
Good to Know!Geometric formulas are used to evaluate quantities such as perimeter, area or volume.
Example The area of a rectangle is equal to the length of the rectangle times the width. As a formula this is written…
A = lw
Vocabulary
Explore! Using Formulas
Step 1 Look at the three shapes above. Can you name the shapes? Identify what you think the variables in each of the geometric formulas represent. Compare with your classmates.
Step 2 On the rectangle above, let l = 6 and w = 2. Use the given geometric formula to find the area of this rectangle.
Step 3 Using the values of l and w from Step 2, find the perimeter of the rectangle using the perimeter formula.
Explore! Using Formulas
Step 4 Find the area of the triangle when b = 10 and h = 3.
Step 5 Find the volume of the rectangular prism above when l = 5, w = 4 and h = 3.
Step 6 Find the surface area of the rectangular prism using the values for l, w and h in Step 5.
Evaluate the formula when given the values for the variables.
a. Find the area of a triangle when b = 12 and h = 4.
Use the formula for thearea of a triangle.
12
12
12
Area
(12)(4)
(48)
24 square units
bh
Example 1
Area is labeled with square units. The units on perimeter are not squared.
Evaluate the formula when given the values for the variables.
b. Find the area and perimeter of a rectangle when l = 9 cm and w = 5 cm.
Use the formula for the areaof a rectangle.
Area
(9)(5)
45 square centimeters
lw
Example 1 Continued…
Evaluate the formula when given the values for the variables.
b. Find the area and perimeter of a rectangle when l = 9 cm and w = 5 cm.
Use the formula for theperimeter of a rectangle.
Perimeter 2 2
2(9) 2(5)
18 10
28 centimeters
l w
Example 1 Continued…
Evaluate the formula when given the values for the variables.
c. Find the area and circumference of a circle whenr = 3 inches. Use 3.14 for .
Use the formula for thearea of a circle.
2
2
Area
(3.14)(3 )
(3.14)(9)
28.26 square inches
r
Example 1 Continued…
Evaluate the formula when given the values for the variables.
c. Find the area and circumference of a circle whenr = 3 inches. Use 3.14 for .
Use the formula for thecircumference of a circle.
Circumference 2
2(3.14)(3)
2(9.42)
18.84 inches
r
Example 1 Continued…
A cereal manufacturer is introducing its new breakfast cereal, Strawberry Crunchettes. The box the cereal will be sold in has a length of 12 inches, a width of 4 inches and a height of 15 inches.
a. Find the volume of the box using the formula: V = lwh. This is how much cereal the box will hold in cubic inches.
The volume of the box is foundby substituting 12 for l, 4 for wand 15 for h.
The volume of the cereal box is 720 cubic inches.
Example 2
V
(12)(4)(15)
720 cubic inches
lwh
A cereal manufacturer is introducing its new breakfast cereal, Strawberry Crunchettes. The box the cereal will be sold in has a length of 12 inches, a width of 4 inches and a height of 15 inches.
b. Find the surface area of the box using the formula: Surface Area = 2(lw + wh + hl). This represents the amount of cardboard needed to make the box.
The surface area of the boxis found by substitutingthe same numbers into thesurface area formula.
The surface area of the cereal box is 576 square inches.
Example 2 Continued…
Surface Area 2( )
2(12 4 4 15 15 12)
2(48 60 180)
576 square inches
lw wh hl
What are two real-world situations where you might need to find the perimeter or area of an object? Describe each situation.
Communication Prompt
1. Find the area of a circle when r = 3 cm. Use 3.14 for π.
2. Find the perimeter of a rectangle when l = 12 and w = 7.
3. Find the area of a triangle when b = 10 and h = 4.
Exit Problems
38 units
28.26 square cm
20 square units