Solving exercises on pages 177 and 178 of Math 2 textbook

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Ngày cập nhật gần nhất: 15/4/2026

Come to the section of solving exercises on pages 177 and 178 of Math 2 textbook, Further Geometry Review, we will continue to reinforce geometric concepts with various calculation exercises involving line lengths, polygons, and perimeter calculations of triangles and quadrilaterals.

Solving exercise 1 on pages 177 and 178 of Math 2 textbook

Problem:

Calculate the lengths of the following polygonal paths:

Answer:

a) The length of polygonal path ABCD is:

3 + 2 + 4 = 9 (cm)

Answer: 9cm.

b) The length of polygonal path GHKM is:

20 + 20 + 20 + 20 = 80 (mm)

Answer: 80mm.

Solving exercise 2 on pages 177 and 178 of Math 2 textbook

Problem:

Find the perimeter of triangle ABC, given the lengths of its sides:

AB = 30cm, BC = 15cm, AC = 35cm.

Answer:

The perimeter of triangle ABC is:

30 + 15 + 35 = 80 (cm)

Answer: 80 cm.

Solving exercise 3 on pages 177 and 178 of Math 2 textbook

Problem:

Find the perimeter of quadrilateral MNPQ, knowing that each side of the shape measures 5cm.

Answer:

The perimeter of quadrilateral MNPQ is:

5 + 5 + 5 + 5 = 20 (cm)

Answer: 20cm.

(Alternatively, you can calculate: 5 x 4 = 20 cm)

Solving exercise 4 on pages 177 and 178 of Math 2 textbook

Problem:

Let's guess which route the ant takes from A to C, either along the polygonal path ABC or along the polygonal path AMNOPQC, which one is longer.

Answer:

Estimating visually, we observe:

The total length of line segments MN, OP, QC equals the length of line segment AB.

The total length of line segments AM, NO, PQ equals the length of line segment BC.

Thus, the lengths of the two polygonal paths ABC and AMNOPQC are equal.

The length of polygonal path ABC is:

5 + 6 = 11 (cm)

The length of polygonal path AMNOPQC is:

2 + 2 + 2 + 2 + 2 + 1 = 11 (cm)

So the lengths of the two polygonal paths are equal.

Solving exercise 5 on pages 177, 178 of Math 2 textbook

Problem:

Arrange 4 triangles into an arrow shape (see illustration):

Answer:

The shapes can be arranged as follows:

Above is the suggestion for solving exercises on pages 177, 178 of Math 2 textbook with detailed instructions. Prepare for solving exercises on page 178 of Math 2 textbook and exercises on page 180 of Math 2 textbook to improve your Math 2 skills.

Detailed instructions for solving exercises on page 45 of Math 2 textbook have been provided for your reference and preparation to better practice Math 2.

Additionally, solving exercises on page 49 of Math 2 textbook is a crucial lesson in the Math 2 curriculum that students should pay special attention to.

Frequently Asked Questions

What are the steps for calculating the perimeter of triangle ABC in the Math 2 textbook?

To calculate the perimeter of triangle ABC, simply add the lengths of its sides. Given AB = 30 cm, BC = 15 cm, and AC = 35 cm, the perimeter is 30 + 15 + 35 = 80 cm.

How can students find the lengths of polygonal paths in the Math 2 exercises?

Students can find the lengths of polygonal paths by adding the lengths of each individual segment. For instance, the length of polygonal path ABCD is calculated as 3 cm + 2 cm + 4 cm, resulting in 9 cm.

Is there a specific method for calculating the perimeter of quadrilateral MNPQ in the textbook?

Yes, to calculate the perimeter of quadrilateral MNPQ, add the lengths of all four sides. With each side measuring 5 cm, the total perimeter is 5 cm + 5 cm + 5 cm + 5 cm, which equals 20 cm.

What is the conclusion about the lengths of polygonal paths ABC and AMNOPQC in the exercises?

Both polygonal paths ABC and AMNOPQC have equal lengths. By calculating the lengths, we find both paths measure 11 cm, indicating they are the same length despite differing shapes.

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