Practice the problems of Math in Focus Grade 5 Workbook Answer Key Chapter 6 Area to score better marks in the exam.

## Math in Focus Grade 5 Chapter 6 Answer Key Area

**Math Journal**

Question 1.

Four students found the area of the shaded triangle.

These are their findings.

Zach: 4 × 4 = 16 cm^{2}

Preeti: \(\frac{1}{2}\) × 5 × 4 = 10 cm^{2}

Brian: \(\frac{1}{2}\) × 7 × 4 = 14 cm^{2}

James: \(\frac{1}{2}\) × 3 × 4 = 6 cm^{2}

Explain the mistakes they have made. Then write the correct answer.

Zach: ________

Preeti: __________

Brian: ______

James: ________

The area of the shaded triangle is: ________

Answer:

Zach: He didn’t consider the fraction 1/2 to calculate the area of the triangle.

Preeti: Base of the triangle is not 5. Hence the answer provided is wrong.

Brain: Base of the triangle is not 7. Hence the answer provided is wrong.

James: Base of the triangle is not 3. Hence the answer provided is wrong.

Area of the shaded triangle = 1/2 × b × h

= 1/2 × 4 × 4

= 8 cm^{2
}

Question 2.

The area of the shaded triangle is 15 square centimeters. Explain why the area of the rectangle is 30 square centimeters.

Answer:

Area of the triangle = 1/2 × base × height

Area of the rectangle = base × height

= 2 × (1/2 × b × h)

= 2 × Area of triangle

= 2 × 15 cm^{2}

= 30 cm^{2}

Question 3.

ABCD is a rectangle and BE = EC.

What can you say about the areas of triangles BED and ECD? Explain your answer.

Answer:

Base and height are same for both the triangles. So, area (1/2 × b × h) of the both triangles will be same.

**Put on Your Thinking Cap!**

**Challenging Practice**

**Solve. Show your work.**

Question 1.

ABCD is a square of side 10 centimeters and BE = EC. Find the area of the shaded triangle.

Answer:

Explanation:

In the above image we can observe ABCD is a square of side 10 centimeters and BE = EC.

Area = 1/2 x b x h

1/2 x 5 x 10

**25 square centimeters**

Area of the shaded triangle is 25 square centimeters.

Question 2.

ABCD is a rectangle 18 centimeters by 8 centimeters. AE = ED and AF = FB. Find the area of the shaded triangle.

Answer:

Explanation:

In the above image we can observe ABCD is a rectangle 18 centimeters by 8 centimeters. Here AE = ED and

AF = FB.

Area = 1/2 x b x h

1/2 x 4 x 9

**18 square centimeters**

The area of the shaded triangle is 18 square centimeters.

Question 3.

ABCD is a rectangle of area 48 square inches. The length of CD is 3 times the length of DF. BC = 4 inches.

a. Find the length of DF.

Answer:

Explanation:

ABCD is a rectangle of area 48 square inches. The length of CD is 3 times the length of DF. Here BC = 4 inches.

The length of DF is** 4 inches**.

b. Find the area of the shaded triangle.

Answer:

Explanation:

In the above image, we can observe ABCD is a rectangle of area 48 square inches. The length of CD is 3 times the length of DF. Here BC = 4 inches.

Area = 1/2 x b x h

1/2 x 4 x 4

**8 square inches**

Area of the shaded triangle is 8 square inches.

Question 4.

ABCD is a rectangle 12 centimeters by 5 centimeters. BE = 4 centimeters. Find the area of the shaded region, ABED.

Answer:

Explanation:

In the above image, we can observe ABCD is a rectangle 12 centimeters by 5 centimeters. Here BE = 4 centimeters.

Area of unshaded region = 1/2 x b x h

1/2 x 8 x 5

**20 square centimeters**

Area of shaded region = 12 x 5 – 20

60 – 20

**40 square centimeters**

The area of the shaded region is 40 square centimeters.

Question 5.

The side of square ABCD is 8 centimeters. AE = AF = 4 centimeters. Find the area of the shaded triangle, CEF.

Answer:

Explanation:

In the above image we can observe the side of square ABCD is 8 centimeters. Here AE = AF = 4 centimeters.

**Area of a square = 8 x 8 = 64 square centimeters**

Area of a triangle a = 1/2 x b x h

a = 1/2 x 4 x 4

**a = 8 square centimeters**

Area of triangle b = 1/2 x b x h

b = 1/2 x 8 x 4

**b = 16 square centimeters**

Area of triangle c = 1/2 x b x h

c = 1/2 x 8 x 4

**c = 16 square centimeters**

Area of shaded triangle = 64 – 8 – 16 – 16

**Area of shaded triangle =24 square centimeters**

Question 6.

The perimeter of rectangle ABCD is 256 inches. Its length is 3 times as long as its width. Find the area of triangle ABC.

Answer:

Explanation:

In the above image we can observe the perimeter of the rectangle ABCD is 256 inches. Its length is 3 times as long as its width.

We know that **8 units = 256 inches**

4 units = 128 inches

2 units = 64 inches

1 unit = 32 inches

Here** width = 32 inches**

**Length = 32 x 3 = 96 inches**

Area of the triangle ABC = 32 x 96 = **3,072 inches**

Question 7.

ABCD is a rectangle of area 72 square centimeters. The length of AD is 3 times the length of AE. BF = 8 centimeters.

a. Find the width of the rectangle.

Answer:

Explanation:

In the above image we can observe ABCD is a rectangle of area **72 square centimeters**.

The length of AD is 3 times the length of AE. Here BF = 8 centimeters.

**Width of the rectangle = 72/12 = 7 cm**

b. Find the area of the shaded region, EBFD.

Answer:

Explanation:

We know that width is equal to 7cm.

Area of the shaded region EBFD = 8 x 7 = **56 square centimeters**

**Put On Your Thinking Cap!**

**Problem Solving**

Question 1.

Look at the pattern of these triangles.

What is the area of Triangle 5 in the pattern? _____

Which triangle in the pattern will have an area of 32,768 square centimeters? _____

Answer:

The Triangle 5 has the base as 32 cm and height as 32 cm.

The area of the Triangle 5 = 1/2 x base x height

1/2 x 32 x 32

512 square centimeters

**The area of the Triangle 5 is 512 square centimeters.**

The Triangle 6 has the base as 64 cm and height as 64 cm.

The area of the Triangle 6 = 1/2 x base x height

1/2 x 64 x 64

2,048 square centimeters

**The area of the Triangle 6 is 2,048 square centimeters.**

The Triangle 7 has the base as 128 cm and height as 128 cm.

The area of the Triangle 7 = 1/2 x base x height

1/2 x 128 x 128

8,192 square centimeters**
The area of the Triangle 7 is 8,192 square centimeters.
**The Triangle 8 has a base as 256 cm and a height of 256 cm.

The area of the Triangle 8 = 1/2 x base x height

1/2 x 256 x 256

32,768 square centimeters

**The area of the Triangle 8 is 32,768 square centimeters.**

The

**triangle 8**in the pattern will have an area of 32,768 square centimeters.

Question 2.

ABCD is a square with sides of 20 centimeters. AX = XB, BY = YC, CZ = ZD, AW = WD. WY and XZ are straight lines. Find the total area of the shaded parts.

Answer:

Explanation:

In the above image, we can observe ABCD is a square with sides of 20 centimeters.

Here AX = XB, BY = YC, CZ = ZD, AW = WD. WY and XZ are straight lines.

The area of triangle WDC = 1/2 x 10 x 20 = 100 square centimeters

The area of triangle WPQ = 1/2 x 5 x 10 = 25 square centimeters

The area of triangle XPB = 25 square centimeters

Area of the shaded region = Area of the whole square – Area of WDC – Area of WPQ – Area of XPB

20 x 20 – 100 – 25 – 25

400 – 100 – 25 – 25

250 square centimeters

Area of the shaded region = 250 square centimeters.

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