1. Evaluating Geometric Formulas Core Focus on Introductory Algebra Lesson 2.3

2. Evaluate each expression. 1.2x − 5 when x = 11 2. when b = 18 3.2l + 2w when l = 5 and w = 3 Warm-Up 17 4 16

3. Evaluating Geometric Formulas Use geometric formulas to find area, perimeter and volume. Lesson 2.3

4. Formula An 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. ExampleThe area of a rectangle is equal to the length of the rectangle times the width. As a formula this is written… A = lw Vocabulary

5. Step 1Look 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 2On the rectangle above, let l = 6 and w = 2. Use the given geometric formula to find the area of this rectangle. Step 3Using the values of l and w from Step 2, find the perimeter of the rectangle using the perimeter formula.

6. Step 4Find the area of the triangle when b = 10 and h = 3. Step 5Find the volume of the rectangular prism above when l = 5, w = 4 and h = 3. Step 6Find the surface area of the rectangular prism using the values for l, w and h in Step 5.

7. 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 the area of a triangle. Example 1 Area is labeled with square units. The units on perimeter are not squared.

8. 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 area of a rectangle. Example 1 Continued…

9. 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 perimeter of a rectangle. Example 1 Continued…

10. Evaluate the formula when given the values for the variables. c.Find the area and circumference of a circle when r = 3 inches. Use 3.14 for . Use the formula for the area of a circle. Example 1 Continued…

11. Evaluate the formula when given the values for the variables. c.Find the area and circumference of a circle when r = 3 inches. Use 3.14 for . Use the formula for the circumference of a circle. Example 1 Continued…

12. 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 found by substituting 12 for l, 4 for w and 15 for h. The volume of the cereal box is 720 cubic inches. Example 2

13. 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 box is found by substituting the same numbers into the surface area formula. The surface area of the cereal box is 576 square inches. Example 2 Continued…

14. What are two real-world situations where you might need to find the perimeter or area of an object? Describe each situation. Communication Prompt

15. 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