Math with Measurements – Area II
Directions: Below is a scale drawing of a home. Use the scale drawing to answer the given questions. The scale is 1 inch = 10 feet
- If you wanted to put crown molding around the ceiling of the master bedroom, how much crown molding should you buy?
60 feet of crown molding is needed.
- If crown molding sells for $3.89/ft., how much will the crown molding cost you?
3.89 × 60 = $233.40
- What is the perimeter of the bathroom (not the master bath)?
4 ¼ inches (1.5 × 2 + 5/8 × 2) which in real life translates to 42.5 feet.
- There is a shrub that you want to put all the way around the perimeter of the home shown. The nursery recommends that the shrub be planted every three feet.
(a) What is the perimeter of the home? 180 feet
(b) How many shrubs should you buy in order to meet the specifications of the nursery? 180 feet ÷ 3 feet means we need to buy about 60 shrubs. Explain how you got your answer.
Since we already know the area of a rectangle to be A = lw, let us apply it to the newly altered parallelogram. The base of the original parallelogram is now the length of the rectangle. The height of the parallelogram is now the width of the rectangle. Using the names base and height instead of length and width, we see that the area of a parallelogram is A = bh.
The area of a triangle can be found by noting that it is simply half of a parallelogram formed by the procedures shown at the left. Therefore, the area of a triangle is A = ½bh.
The procedure to find the area of a quadrilateral with only one pair of parallel sides (trapezoid) is very similar. To form a parallelogram using a trapezoid, make a copy of a trapezoid and then rotate it 180 degrees and make the corresponding sides coincide as shown below.
The area of a parallelogram above is . Since the area of the parallelogram above is twice the area of the trapezoid, we divide it by 2 making the area of the trapezoid
.
A circle is the locus of all points in a plane that are equidistant from a point. The equidistant amount is known to be the radius of a circle.
Let's start at the center of a circle and cut it into an even number of equally sized pie-shaped wedges. If we arrange these wedges so they lie next to each other such that they alternate pointed up and down and up again until all the wedges are used, the resulting figure will resemble a parallelogram. The more wedges we have, the smaller each wedge will be and a better looking parallelogram will result. As the number of wedges increases, a cleaner picture more closely resembling a parallelogram would form. Only when an infinite number of wedges were used could a perfect parallelogram be constructed.
- If AL represents the area of the triangle on the left and AR represents the area of the triangle on the right, which of the two has larger area or they are equal or you cannot make the comparison without additional information.
Answer: they are equal because they have the same base and height.
- What is the sum of the areas of the five shaded triangles shown at the right that are drawn interior to a 3 by 6 rectangle?
Answer: 9.
All five triangles share the same height (3) and their bases together is the same as the length of the rectangle (6). Hence the area is ½ × 3 × 6 = 9
- The figure shows a shaded rectangle inside a parallelogram. What is the area of the shaded rectangle? (8 – 3) × 4 = 20 sq. cm.
- What fraction of the circle is shaded?
- Between 0 and ¼
- Between ¼ and ½
- Between ½ and ¾
- Between ¾ and 1
- Find the area of the curved section of the sidewalk.
6’6” = 6.5’
Area = ¼ × π × 6.52 ≈ 33.18sq. in.
- In the below figure, ABCD is a rectangle, and circles P and Q each have a radius of 5 cm. What is the area of the rectangle?
length = 20; width = 10Area = 200 cm2
- A square with 24 inch on each side.
(a) What is the area of the square?
24 × 24 = 576 sq. in
(b) What is the radius r of the circles?
24 ÷ 4 = 6 in.
(c) What is the area of a circle r?
A=πr2 = π × 36 = 36π sq. in.
(d) What is the area remaining when you remove 4 circles of radius r from the square?
576 – 4 × 36π ≈ 123.6 sq. in.
- The outside diameter of a concrete floor for a circular silo is 14 feet 6 inches and the wall is 6 inches thick. What is the area of the silo?
¼ ×π × (14.52 – 13.52) ≈21.99 sq. in.
- Ron plans to hire a lawn service to mow his yard. It costs $0.06 per square meter to have the lawn mowed. Using the diagram of Ron’s lot, calculate the cost of the mowing service.
Area A: 24.7 × 20 = 494m2
Area of the house: 13 × 17 = 221m2
Area “A” of the yard = 494 – 221 = 273 m2
Area B: 13.5 × 13.6 = 183.6m2
Area C: ½ × 13.5 × (20– 13.6) = 43.2m2
Total Area to be mowed: 273 + 83.6 + 43.2 = 499.8m2
Total Cost: 499.8 × $0.06 = $29.99
8. The net of a rectangular prism is shown below.
- What is the total surface area of the rectangular prism represented by this net?
3.1 × 5 × 2 + 7.4 × 5 × 2 + 3.1 × 7.4 × 2 =
- What is the total volume of the rectangular prism represented by this net?
3.1 × 5 × 7.4 =
11. In Figure 1 a cylinder with a diameter of 12 centimeters is filled with water to a height of 8 centimeters. In Figure 2 a rock is submerged in the cylinder. Which of the following is closest to the volume of the rock?
- 139 cm3
- 418 cm3
- 1674 cm3
- 1323 cm3
Estimate the area of Antarctica using the map scale.
between 12 000 000 sqkms and 18 000 000 sqkms
9. You are building a racing engine for a customer and he wants more cubic inches. You have an eight-cylinder engine with a bore of 4.00 inches and a stroke of 3.50 inches. You are given the formula for engine displacement of (Bore/2) squared times π times stroke times number of cylinders.
Volume of a cylinder = πr2L (L is the stroke length.)
A. What is the cubic inches of the stock motor? ______
B. What is the cubic inches if the bore is increased by 0.120 inches? ______
C. What is the cubic inches if a crankshaft with a stroke of 3.750 inches is used? ______
D. It costs $160 to bore a motor and buy pistons or $399 to buy a longer stroke crank. What would you tell the customer who wants more cubic inches but wants it cheap? ______
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