This handy Math in Focus Grade 3 Workbook Answer Key Chapter 19 Area and Perimeter provides detailed solutions for the textbook questions.

## Math in Focus Grade 3 Chapter 19 Answer Key Area and Perimeter

**Math Journal**

**Look at John’s answers for the perimeter of the squares and rectangles.**

John’s mistakes are circled. Explain why his answers are not correct.

Answer:

John added only two sides to find perimeter,

the perimeter formulas for rectangles and square.

The perimeter of a rectangle is the total distance of its outer boundary.

It is twice the sum of its length and width and it is calculated with the help of the formula:

Perimeter = 2(length + width).

Explanation:

The perimeter of a square is defined as the total length that its boundary covers

The formula to calculate the perimeter of a** **square is as, mathematically expressed as;

Perimeter of square, (P) = 4 × Side

**Write the correct answers.**

**Example** The unit for the perimeter of Figure B should be meter (m).

Question 1.

Perimeter of Figure A: _____________________

Answer: 20 cm

Explanation:

The perimeter of a rectangle is the total distance of its outer boundary.

It is twice the sum of its length and width and it is calculated with the help of the formula.

Perimeter = 2(length + width).

P=2(6 + 4) = 2 x 10 = 20cm

Question 2.

Perimeter of Figure C: _____________________

Answer: 20 cm

Explanation:

The perimeter of a square is defined as the total length that its boundary covers

The formula to calculate the perimeter of a** **square is as, mathematically expressed as;

Perimeter of square, (P) = 4 × Side

P = 4 x s

= 4 x 5 = 20 cm

Question 3.

Perimeter of Figure E: _____________________

Answer: 20cm

Explanation:

The perimeter of a square is defined as the total length that its boundary covers.

The formula to calculate the perimeter of a** **square is as, mathematically expressed as;

Perimeter of square, (P) = 4 × Side

**Put On Your Thinking Cap!**

**Challenging Practice**

**Complete.**

Question 1.

Draw different rectangles with an area of 12 square centimeters. Then draw different rectangles with an area of 9 square centimeters. How many rectangles can you draw for each area?

Answer:

2 rectangles can be drawn for area of area 12 square centimeters and,

1 rectangle can be drawn for area of 9 square centimeters.

Explanation:

The area of rectangle (A) is the product of its length ‘a’ and width or breadth ‘b’.

So, Area of Rectangle = (a × b) square units.

The square is a shape with four equal sides.

The area of a square is defined as the number of square units that make a complete square.

It is calculated by using the formula Area = s × s = s^{2} in square units.

So, area = 9 square centimeters.

**Solve.**

Question 2.

Karl bends a piece of wire into a square as shown.

Answer: 32cm

Explanation:

The perimeter of a square is defined as the total length that its boundary covers,

The formula to calculate the perimeter of a** **square is as, mathematically expressed as;

Perimeter of square, (P) = 4 × Side

P = 4 x 8 = 32 cm

Which of these rectangles can he make using the same piece of wire?

Answer:

Rectangle B and C perimeter is 32cm.

Explanation:

Perimeter of rectangle A

Perimeter = 2(length + width).

P=2(8 + 4) = 2 x 12 = 24cm

Perimeter of rectangle B

Perimeter = 2(length + width).

P=2(10 + 6) = 2 x 16 = 32cm

Perimeter of rectangle C

Perimeter = 2(length + width).

P=2(11 + 5) = 2 x 16 = 32cm

Perimeter of rectangle D

Perimeter = 2(length + width).

P=2(9 + 8) = 2 x 17 = 34cm

Question 3.

Ally wants to build an exercise pen for her pet rabbit. She has 36 feet of fencing to build a rectangular enclosure in her yard. She wants to carefully plan the length and width of the pen, measuring in units of whole feet.

**Find all the possible ways that Ally could build her pen and have a perimeter of 36 feet. Fill in the table below.**

Answer:

Explanation:

Ally wants to build an exercise pen for her pet rabbit.

So, Perimeter = 2(length + width)

Perimeter = 2(1 + 17) = 36 ft

Perimeter = 2(2 + 16) = 36 ft

Perimeter = 2(3 + 15) = 36 ft

Perimeter = 2(4 + 14) = 36 ft

Perimeter = 2(5 + 13) = 36 ft

Perimeter = 2(6 + 12) = 36 ft

Perimeter = 2(7 + 11) = 36 ft

Perimeter = 2(8 + 10) = 36 ft

Perimeter = 2(9 + 9) = 36 ft

Question 4.

What are some of the concerns that Ally needs to think of in planning for the exercise pen?

Answer:

Perimeter and area of exercise pen.

length and width of exercise pen.

Explanation:

The above are some of the concerns that Ally needs to think of in planning for the exercise pen.

**Put On Your Thinking Cap!**

**Problem Solving**

**Solve. Look at this pattern.**

What is the area of each figure?

Answer:

Explanation:

In the above picture each area of the square is measured as 1 square centimeter.

In figure A there is only 1 square box.

In figure B there are 3 square boxes.

In figure C there are 5 square boxes.

If the pattern continues, what will the area of Figure E be? Draw Figure E below.

Answer:

the area of Figure D & E

Explanation:

In the above picture each area of the square is measured as 1 square centimeter.

In figure D there are 7 square units.

In figure E there are 9 square units.

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