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Answer :
Problem 1: (b) 96 m²
Problem 2: (a) 1.4 gallons (rounded to nearest whole number)
Problem 3: (a) 580.125 cm³
Problem 4: (a) 242 sq. ft.
Problem 5: (a) 6, 8, and 9 inches
Let's solve these problems step-by-step.
Problem 1: Area of a triangle with base 16 m and altitude of 12 m.
Steps to solve:
a. Recall the formula for the area of a triangle:
Area = 1/2 × base × height
b. Substitute the given values:
Area = 1/2 × 16 m × 12 m
c. Simplify the expression:
Area = 96 m²
Problem 2:
You wish to paint storage shed. Its 4 walls measure 7 ft. high, 8 ft wide each. If 1 gallon paint covers 160 sq. ft., how many gallons of paint will you need?
Steps to solve:
a. Calculate the total wall area:
Total area = 2 × (height × width) × number of walls
b. Substitute the given values:
Total area = 2 × (7 ft × 8 ft) × 4
c. Simplify the expression:
Total area = 224 sq. ft.
d. Divide the total area by the area covered by one gallon of paint: Number of gallons = Total area / Area covered per gallon
e. Substitute the values:
Number of gallons = 224 sq. ft. / 160 sq. ft./gallon
f. Simplify the expression:
Number of gallons = 1.4 gallons
Problem 3: Find the volume of the following solid figure. A rectangular solid has sides of 10.5 cm, 6.5 cm, and 8.5 cm. What is its volume?
Steps to solve:
a. Recall the formula for the volume of a rectangular solid:
Volume = length × width × height
b. Substitute the given values:
Volume = 10.5 cm × 6.5 cm × 8.5 cm
c. Simplify the expression:
Volume = 580.125 cm³
Problem 4:
Work following area application problem. You are laying an asphalt driveway. How much area must you cover if the driveway is 22 feet long and 11 feet wide?
Steps to solve:
Calculate the area of the driveway: Area = length × width
Substitute the given values: Area = 22 ft × 11 ft
Simplify the expression: Area = 242 sq. ft.
Problem 5:
Suppose you want to represent a triangle with sides 12 feet, 16 feet, and 18 feet on a drawing where 1 inch = 2 feet. How long should the sides of the triangle be in inches?
Steps to solve:
a. Divide each side of the triangle by the scale factor:
New side length = Original side length / Scale factor
b. Substitute the given values:
New side length 1 = 12 ft / 2 ft/in, New side length 2 = 16 ft / 2 ft/in, New side length 3 = 18 ft / 2 ft/in
c. Simplify the expressions:
New side length1 = 6 in,New side length2 = 8 in,New side length3 = 9 in
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