Mathematics
Grade 6
15 min
Area between two rectangles
Area between two rectangles
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Introduction & Learning Objectives
Learning Objectives
Define and identify the 'area between two rectangles'.
Calculate the area of a single rectangle using its length and width.
Apply the subtraction principle to find the area of a region formed by one rectangle inside another.
Solve word problems involving finding the area between two rectangles.
Correctly label area measurements with appropriate square units.
Differentiate between the area of a rectangle and its perimeter.
Have you ever seen a picture frame or a mat around a photo? 🖼️ How much space does the mat itself cover, not including the photo?
In this lesson, you'll learn how to calculate the space between two rectangular shapes, especially when one is placed inside another. This skill helps us understand and measure parts of composi...
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Key Concepts & Vocabulary
TermDefinitionExample
RectangleA four-sided flat shape with all angles being right angles (90 degrees) and opposite sides being equal in length.A standard piece of paper, a door, or a computer screen are all examples of rectangles.
AreaThe amount of two-dimensional space a flat shape covers, measured in square units.If a square has sides of 1 inch, its area is 1 square inch. The area of your classroom floor is the space it covers.
Length (l)The longer side of a rectangle, or one of its dimensions.If a rectangle is 10 cm long and 5 cm wide, its length is 10 cm.
Width (w)The shorter side of a rectangle, or one of its dimensions.If a rectangle is 10 cm long and 5 cm wide, its width is 5 cm.
Square UnitsThe units used to measure area, indicating how many squares of a certain size fit inside a...
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Core Formulas
Area of a Rectangle
$$A = l \times w$$
To find the area (A) of any rectangle, multiply its length (l) by its width (w). Remember to use consistent units.
Area Between Two Rectangles
$$A_{between} = A_{larger} - A_{smaller}$$
To find the area of the region between two rectangles (where one is inside the other), first calculate the area of the larger rectangle, then calculate the area of the smaller rectangle, and finally subtract the smaller area from the larger area.
4 more steps in this tutorial
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Challenging
A design consists of three concentric rectangles. The largest is 20x16 units. The middle is 16x12 units. The smallest is 10x6 units. What is the area of the region that is inside the middle rectangle but outside the smallest rectangle?
A.320 units²
B.128 units²
C.132 units²
D.60 units²
Challenging
A homeowner is building a brick border around a rectangular patio. The patio is 15 feet by 12 feet. The brick border makes the total area 13 feet by 10 feet larger. Wait, that's not right. Let's rephrase. A homeowner is building a brick border around a rectangular patio. The patio itself is 13 feet by 10 feet. The border adds 1 foot to each side, making the outer dimensions 15 feet by 12 feet. If the bricks cost $3 per square foot, what is the total cost of the bricks for the border?
A.$390
B.$150
C.$540
D.$50
Challenging
A rectangular frame has outer dimensions of 13 inches by 11 inches. The area of the matting inside the frame is 80 square inches. If the matting forms a uniform border, what is the width of that border?
A.1 inch
B.1.5 inches
C.2 inches
D.2.5 inches
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