# 6th Grade - Use Variables In Formulas

 Grade Level: 6th Skill: Algebra Topic: Use Variables in Formulas Goal: Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1 - 2bh, C = Pi*d - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Skill Description: Use variables (symbols/letters), along with the correct formula to write expressions for: perimeter, area and circumference in algebraic terms. Understand that a set formula will always be used to solve problems involving: perimeter, area or circumference. Memorize and use the formula for perimeter; area of a circle, square, rectangle, and triangle; and circumference of a circle.

## Building Blocks/Prerequisites

### Sample Problems

 (1) t  s What is the area of the triangle above? Express the answer algebraically. (t x s  2) (2) A square has four sides with the value of s. How would you solve to find the perimeter? (s + s + s + s, 4s) (3) If a circle has the diameter of x, what is its circumference? (C  x) (4) Which is the correct algebraic representation for the area of a circle? (a) A = d (b) A = rr (c) A =  r2 (b) (5) A rectangle has width (w). Its length is 4 times more than its width. Find the perimeter of the rectangle. (Your answer will be expressed in terms of w. ) (w + w + 4w + 4w or 2w + 2(4w))

### Online Resources

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### Extra Help Problems

 (1) A rectangle has the width of x and length of y, which best algebraic representation to find area? (a) A = x + y (b) A = xy (c) A = 2x + 2y (b) (2) How many ways could you write the formula to find the perimeter of a square with sides that have a measure of b? (two; b+b+b+b or 4b) (3) An equilateral triangle has sides that measure y, which best algebraic representation to find perimeter? (a) 3y (b) 2y (c) y + y + y + y (a) (4) A right triangle has a base m and height n. How could this be written as a formula to show the area? (m x n  2 or ½ mn) (5) A circle has the diameter, d, which formula could be used to find circumference? (a) r 2 (b) d2 (c) r (d) d (d) (6) A triangle has a base with a measure of b and a height of h. Which formula could be used to show area? (a) b x h  2 (b) b x h (c) b x h x 2 (d) b x h + ½ (a) (7) There is a trapezoid with the following measures: base 1 - s; base 2 – t, height – h. Which formula could be used to find area? (a) (s + t) + h x ½ (b) ½ (s + t)h (c) s x t x h (b) (8) Write an expression to find the perimeter for a trapezoid where b1 = a, b2 = b, h=4 ((a + b) 4  2or ½ (a + b) 4) (9) A square has a side = x. Write a formula to find the area for this square. (xx) (10) A rectangle has a width (w) ½ the size of its length (L). Which formula could be use to show perimeter? (a) P = ½ w + L (b) P = (½ L 2) + L2 (c) 2L  2w1/2 (b) (11) A circle has a radius worth, y. Write a formula to solve for area. (A   y 2 ) (12) A circle has the radius worth r, which formula would show how to use this to find circumference? (a) (r  2) (b) r  2) (c) r 2 (a) (13) A circle has a diameter, measuring d. Write a formula to find the area. (A   (d2) 2 ) (14) A rectangle has a perimeter of 60. Write a formula to show perimeter, if length is 5 times greater than the width. (60 = 2w + 2 (wx5)) (15) A triangle has a base of 10 cm and height of 4 cm. Use the correct formula to find its area. (A  20 cm2 ) (16) An equilateral triangle has sides (s) worth 6 inches. Write a formula and solve to find its perimeter. (P = 3s, P = 18 in.) (17) A square has sides worth 5 yd. What is its area and perimeter? Explain how the formulas differ for each. (A = 25 yd2 , P = 20 yd) (18) The measures of a rectangle are w = 12 mm, l = 20 mm. Use this information to solve for perimeter and area. Explain your process in solving each. (P = 64 mm, A = 240 mm2 ) (19) The measures of a triangle have a base of 11 ft and height of 12 ft. Use this information to solve for area. Could you use the information in this problem to find the perimeter? Explain. (A= 66 sq. ft. No, you can’t find perimeter, you need to know the measures of the sides of the triangle to find the perimeter.) (20) A circle has a diameter measuring 10 inches. Use formulas to find the area and circumference of the circle. Explain the difference between the steps to solve this problem. (C = 31.4 in, A = 78.5 in2 ) (21) Jake is making a frame for his grandparents. The photo he needs to frame has a width of 6 inches and a length of 8 inches. What is the minimum amount of wood Jake needs to build his frame? (28 in.) (22) Angelica is building a fence around her circular garden. The radius of the garden is 3 inches. How much fencing should Angelica buy? (18.84 in.) (23) Timmy has a rectangular patio that he’d like to fill with tiles. It has a length of 6 cm and width of 4 cm. What formula should he use to find out how many centimeters of tiles are needed to fill it? (24 cm2 ) (24) Lisa has a square frame. She’d like to fill the inside of the frame with a decorative fabric. The sides of the frame are 3 yards. How much fabric will Lisa need to fill the frame? (9 yards) (25) Dave is making a triangular wall hanging. The base of the triangular frame is 6 inches, and the height 7 inches. If Dave wants to fill the inside with aluminum, how much will he need? (21 inches2)