All the solutions provided in McGraw Hill My Math Grade 4 Answer Key PDF Chapter 13 Lesson 3 Model Area will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 13 Lesson 3 Model Area
A square with a side length of one unit is called a unit square.
A unit square has one square unit of area and can be used to measure area. Area is the number of square units needed to cover a figure without overlapping.
Draw It
Find the area of the rectangles shown in the table.
1. Draw each rectangle.
Use grid paper to draw each rectangle.
2. Find the length and width of each rectangle.
Count the number of unit squares that cover the length and width of the rectangle. Record each in the table.
3. Determine the area of each rectangle.
Count the number of whole squares that cover the rectangle. Each whole square is 1 square unit.
Answer: Given the figure, find the lengths, widths, and area.
(i) The area of a rectangle for the first figure is,
The figure consists of 1 row and 4 columns.
So, the formula for the area of a rectangle is, l x w
A= 4 x 1 = 4 square units.
(ii) The area of a rectangle for the second figure is,
The figure consists of 2 rows and 4 columns.
So, the formula for the area of a rectangle is, l x w
A= 2 x 4 = 8 square units.
(iii) The area of a rectangle for the third figure is,
The figure consists of 3 rows and 4 columns.
The formula for the area of a rectangle is, l x w
A= 3 x 4 = 12 square units.
(iv) The area of a rectangle for the fourth figure is,
The figure consists of 3 rows and 5 columns.
So, the formula for the area of a rectangle is, l x w
A= 3 x 5 = 15 square units.
Try It
Find a formula that can be used to find the area of a rectangle.
1. Measure the length and width of each object listed in the table.
Use a centimeter ruler to measure the length and the width of each object to the nearest centimeter. Record the results in the table.
2. Find the area of each object.
Use what you learned in the first example to estimate the area of each object. Draw rectangles on grid paper. Then. count the unit squares to find the area. Record the results.
3. Justify the formula for area.
Look for a pattern to find how length and width relate to the area.
The area of each object is the product of the _______________ and ______________.
Answer: Given the figure, which consists of a sticky note, crayon box, and book.
Now, we will find the area of the given objects.
The area of each object is the product of the length and width.
Explanation: (i) The figure of the sticky note is in a square shape.
The formula for the area of a square is s x s
The one side of a square is 4.
So, the area of a square is 4 x 4 = 16 square cm.
(ii)The crayon box is in rectangular shape.
The formula for the area of a rectangle is l x w.
The length and width of a crayon box are 9 cm and 6 cm.
So, the area of a rectangular crayon box is 9 cm x 6 cm = 54 sq.cm
(iii)The book is in a rectangle shape
The area of a rectangle formula is l x w.
The length and width of a book are 10 cm and 8 cm.
So, the area of a book is 10 cm x 8 cm = 54 sq.cm
Talk About It
Question 1.
How did you make your estimates for the areas of the objects in Activity 2? How close were the estimates to the actual areas?
Answer: In Activity 2, based on the shape of the figure make our estimates for the area of the objects. We can estimate the length and width value we get the area easily. The square has both lengths, the widths will be the same. In a rectangle, length and width will be different.
Question 2.
What operation can you use with the length and the width to equal the area of a rectangle? Explain.
Answer: By using the multiplication operation, we can multiply the length and width of a rectangle.
Question 3.
Mathematical PRACTICE Use Symbols What is the formula for the area of a rectangle? Use A for the area, l for length, and w for width.
Answer: The formula for the area of a rectangle is, A = l x w.
Practice
Complete the table below.
Answer: Given the figures,
We will find the area of a rectangle for that figures.
(i)For the first figure, the length is 3 units, and the width is 1 unit.
The formula for the Area of a rectangle is l x w
A = 3 x 1 = 3 sq.units.
(ii)For the second figure, the length is 4 units, width is 5 units.
The formula for the Area of a rectangle is l x w
Area = 4 x 5 = 20 sq.units.
(iii)For the third figure, the length is 6 units, width is 3 units.
The formula for the Area of a rectangle is l x w
Area = 6 x 3 = 18 sq.units.
The figure is,
(iv)For the fourth figure, the figure consists of a length is 6 units, and width is 5 units.
So, the Area of a rectangle formula is l x w
Area = 6 x 5 = 30 sq.units.
(v)For the fifth figure, the length is 7 units, width is 6 units.
The formula for the Area of a rectangle is l x w
Area = 7 x 6 = 42 sq.units.
The figure for the length is 7 units and the width is 6 units.
Apply It
Use the area formula you wrote in Exercise 3 to solve each problem.
Question 9.
Mr. Hart is hanging a picture on a wall. The picture frame has a length of 12 inches and a width of 9 inches. How much wall space will the picture need?
Answer: 108 sq inches of wall space will be needed for the picture.
Explanation: Given that, the picture frame length is 12 in and the width is 9 inches.
The wall space is nothing but the area.
Based on the given length and width.
The picture will be in rectangular shape.
The formula for the area of a rectangle is l x w
A = 12 x 9 = 108 sq. inches.
Question 10.
What is the area of a classroom with a length of 30 feet and a width of 15 feet?
Answer: The area of a classroom is 450 sq. ft
Explanation: Given that, the classroom length is 30 ft and the width is 15 ft.
Based on the given length and width.
The classroom will be in rectangular shape.
So, the formula for the area of a rectangular classroom is l x w.
A = 30 ft x 15 ft = 450 sq.feets
Question 11.
Miss Foster wants to buy carpet for her living room. The living room has a length of 15 feet and a width of 10 feet. How much carpet will she need?
Answer: The carpet Miss Foster needed is 150 sq. ft.
Explanation: Given the living room length is 15 ft and the width is 10 ft.
Based on the given length and width.
The living room will be in rectangular shape.
So, the area of a rectangular classroom formula is l x w.
A = 15 ft x 10 ft = 150 sq.feets
Question 12.
Mathematical PRACTICE Use Math Tools Ricky’s computer monitor is a rectangle. The length is 15 inches and the width is 12 inches. Estimate the area of the monitor.
Answer: The area of a rectangle monitor is 180 sq. inches.
Explanation: Given that, the length of the monitor is 15 inches and the width is 12 inches.
Now, we will find the area of the rectangular monitor.
The area of a rectangle formula is, l x w
So, the area of the rectangular monitor is, 15 x 12 = 180 sq. inches
Write About It
Question 13.
Suppose two rectangles have the same area. Must they have the same length and width? Explain.
Answer: No
Explanation: Two rectangles have the same area but don’t need to have the same length and width.
The length and width of the rectangle are just factor pairs of the number that is the area.
McGraw Hill My Math Grade 4 Chapter 13 Lesson 3 My Homework Answer Key
Practice
Find the area of each rectangle.
Question 1.
A = _____________ square units
Answer: Area = 8 x 3 = 24 sq.units.
Explanation: Given that,
The rectangular figure consists of a length is 3 units and the width is 8 units.
Now, we will find the area of a rectangle.
The formula for the area of a rectangle is length x width.
So, the area is 8 x 3 = 24 sq.units
Question 2.
A = _____________ square units
Answer: Area = 6 x 6 = 36 sq.units
Explanation: Given the square figure,
The figure side is 6 units.
We will find the area of a square.
The formula for the area of a square is S x S
So, the area is 6 x 6 = 36 sq.units
Question 3.
A = _____________
Answer: Area = 11 x 4 = 44 sq.units
Explanation: Given the rectangle figure,
The figure consists of the length is 11 units and the width is 4units.
Now, we will find the area of a rectangle.
The formula for the area of a rectangle is length x width.
So, the area is 11 x 4 = 44 sq.units
Question 4.
A = _____________
Answer: Area = 6 x 7 = 42 sq.units
Explanation: Given the rectangle figure,
The figure consists of a length of 7 units and a width of 6 units.
We will find the area of a rectangle.
The area of a rectangle formula is length x width.
So, the area is 6 x 7 = 42 sq.units
Problem Solving
Use the area formula A = l × w you discovered in the lesson to solve each problem.
Question 5.
Mathematical PRACTICE Justify Conclusions Three guinea pigs living n the same cage need at least 12 square feet of living space. Is a cage that measures 3 feet by 5 feet big enough for three guinea pigs? Explain.
Answer: Yes, there is enough space. Because pigs living cages needs 12 square feet cage but the actual cage size is 3 x 5 = 15 sq. ft. So, it’s enough.
Explanation: Given that, Three guinea pigs need a 12 sq. ft cage.
But the given cage measurements are 3ft and 5ft.
Based on the given measurements.
The cage will be in rectangular shape.
So, the area of a rectangle formula is length x width.
A = 3 ft x 5ft = 15 sq.ft
Question 6.
Jeanette drew a rectangle with an area of 6 square centimeters. Identify a possible length and width for her rectangle.
Answer: The possible length and width for her rectangle are, (1,6), (2,3), (3,2), and (6,1).
Explanation: Given that, Jeanette drew a rectangle area is 6 sq. cm
We will find the possible length and width of her rectangle.
The formula for the area of a rectangle is length x width.
So, the possible factors of 6 are (1, 6), (2,3) (3,2), and (6,1)
Question 7.
Marcus wants to carpet his clubhouse. One side of the rectangular floor measures 11 feet. Another side measures 8 feet. How many square feet of carpet does Marcus need to completely cover the floor?
Answer: Marcus needs to cover the floor completely by 88 square feet.
Explanation: Given that,
Marcus wants to carpet his clubhouse.
The sides of a rectangular floor are 11 ft and 8 ft.
We will find the area of that rectangular floor.
The area of a rectangular floor formula is length x width.
So, the area is l x w = 11 x 8 = 88 sq.ft
Vocabulary Check
Question 8.
Explain the relationship between area and square units.
Answer: The difference between area and square units is, that the area is the amount of space occupied by an object. A square unit is a square with sides of length is one unit.
Question 9.
Define unit square.
Answer: A unit to measure the area of squares. It has a side that is 1 unit long.