Chapter 3 · Real estate
Area and measurement
Square feet, acres and lots that are not rectangles
Measurement questions come down to one skill: turning a shape into square feet, then converting or pricing it.
Every lot in this chapter is drawn to scale, and the card under the figure shows each multiplication.
3.1 · Rectangles and square feet
Length times width
The area of a rectangle is its length times its width. Both must be in the same unit; feet times feet gives square feet.
area = length × width
Why: Square feet counts how many one-foot squares fit inside the shape.
A lot 150 feet wide and 100 feet deep holds 150 × 100 = 15,000 square feet.
Watch out: Do not add the sides: 150 + 100 + 150 + 100 = 500 feet is the perimeter, used for fencing, not area. A square yard is 9 square feet, not 3.
3.2 · Acres
43,560 square feet to the acre
Divide square feet by 43,560 to get acres; multiply acres by 43,560 to get square feet.
1 acre = 43,560 sq ft
Why: Land is priced and described in acres, but measured in feet.
A parcel 660 feet by 330 feet is 217,800 square feet: 217,800 ÷ 43,560 = 5 acres.
At $24,000 an acre it is worth $120,000.
Watch out: A front foot is measured along the street only. A price per front foot multiplies the frontage, not the area.
3.3 · Irregular lots
Cut it into shapes you can measure
Split an irregular lot into rectangles and triangles, find each area, and add them. A right triangle is half of the rectangle around it.
triangle = ½ × base × height
Why: Every polygon on the exam can be cut into rectangles and right triangles.
Rectangle A is 100 × 60 = 6,000 square feet.
Rectangle B is 40 × 30 = 1,200, and triangle C is ½ × 60 × 30 = 900.
Together: 8,100 square feet.
Watch out: Forgetting the ½ doubles a triangle. And measuring the box around the whole lot counts land that is not there.
3.4 · Price per square foot
Area times the rate
A price per square foot times the area gives the price; the price divided by the area gives the rate.
price = area × price per sq ft
Why: Comparing homes of different sizes is easier on a per-square-foot basis.
A 60-by-40 house is 2,400 square feet. At $210 a square foot it is $504,000.
Watch out: Use the area the rate refers to: living area for a house, lot area for land.
3.5 · One lot, start to finish
Cut it, measure it, convert it, price it
Every measurement question is the same four moves: cut the shape into rectangles and right triangles, multiply each out and add, divide by 43,560 if acres are asked for, and multiply or divide by the rate on the area it refers to.
Why: On the ground the moves are one job: the same tape that measures the lot gives its acres and its price.
Measure a new lot below: choose where to cut it, work each piece and the total, turn the total into acres, measure the L-shaped house, and price the house and the land.
Watch out: The numbers below are a different lot and house from the ones in the sections above, so work each answer rather than recalling it.
You are listing this corner lot and the house on it. Measure the land, turn it into acres, measure the house, and price each by the square foot.
1 / 5 Cut the lot into shapes
The lot fronts the street for 240 feet but is only 160 feet wide at its rear line, 200 feet back. Its west side is square to the street. The road runs along the slanted east side.
| Front line, on the street | 240 ft |
|---|---|
| Rear line | 160 ft |
| West side | 200 ft |
| East side, along the road | 215.4 ft |
The lot is not a rectangle: the road cuts its east side at an angle. How do you measure it?
Practice · Set 1
Each question sets the figure to its own numbers
A lot is 125 feet wide and 200 feet deep. How many square feet is it?
Practice · Set 2
Each question sets the figure to its own numbers
A parcel measures 660 feet by 330 feet. How many acres is it?
Practice · Exam style
Each question sets the figure to its own numbers
A rectangular lot measures 210 feet by 140 feet. How many acres is it, to two decimal places?
- A
- B
- C (triangle)