Practical Geometry Class 8th Mathematics Term 2 Tamilnadu Board Solution

Class 8^th Mathematics Term 2 Tamilnadu Board Solution

Exercise 2.1

1. BE = 5 cm and BS = 8 cm. Draw rhombus BEST with the following measurements and…
2. BE = 6 cm and ET = 8.2 cm. Draw rhombus BEST with the following measurements and…
3. BE = 6 cm and ∠B = 45°. Draw rhombus BEST with the following measurements and…
4. BE = 7.5 cm and ∠E = 65°. Draw rhombus BEST with the following measurements and…
5. BS = 10 cm and ET = 8 cm. Draw rhombus BEST with the following measurements and…
6. BS = 6.8 cm and ET = 8.4 cm. Draw rhombus BEST with the following measurements…
7. BS = 10 cm and ∠B = 60°. Draw rhombus BEST with the following measurements and…
8. ET = 9 cm and ∠E = 70°. Draw rhombus BEST with the following measurements and…

Exercise 2.2

1. JU = 5.4 cm and UM = 4.7 cm. Construct rectangle JUMP with the following…
2. JU = 6 cm and JP = 5 cm. Construct rectangle JUMP with the following…
3. JP = 4.2 cm and MP= 2.8 cm. Construct rectangle JUMP with the following…
4. UM = 3.6 cm and MP = 4.6 cm. Construct rectangle JUMP with the following…
5. MO = 5 cm and diagonal MR = 6.5 cm. Construct rectangle MORE with the following…
6. MO = 4.6 cm and diagonal OE = 5.4 cm. Construct rectangle MORE with the…
7. OR = 3 cm and diagonal MR = 5 cm. Construct rectangle MORE with the following…
8. ME = 4 cm and diagonal OE = 6 cm. Construct rectangle MORE with the following…
9. Side 5.1 cm. Construct square EASY with the following measurements. Find its…
10. Side 3.8 cm. Construct square EASY with the following measurements. Find its…
11. Side 6 cm. Construct square EASY with the following measurements. Find its area…
12. Side 4.5 cm. Construct square EASY with the following measurements. Find its…
13. 4.8 cm. Construct square GOLD, one of whose diagonal is given below. Find its…
14. 3.7 cm. Construct square GOLD, one of whose diagonal is given below. Find its…
15. 5 cm. Construct square GOLD, one of whose diagonal is given below. Find its…
16. 7 cm. Construct square GOLD, one of whose diagonal is given below. Find its…

---

Exercise 2.1

Question 1.

Draw rhombus BEST with the following measurements and calculate its area.

BE = 5 cm and BS = 8 cm.

Answer:

Step 1 – Draw a Line BE of length 5 cm

Step 2 – Draw a circle of Radius 8 cm centered at B.

Step 3 – Draw a circle of radius 5 cm centered at E.

The intersection point of the two circle gives the point S.

Step 4 – Draw lines BT and ST parallel to ES and EB respectively both of length 5 cm.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area = 

Question 2.

Draw rhombus BEST with the following measurements and calculate its area.

BE = 6 cm and ET = 8.2 cm.

Answer:

Step 1 – Draw a line BE of length 6 cm.

Step 2 – Draw a circle of radius 8.2 cm Centered at E and a circle of radius 6 cm centered at B.

Step 3 – Complete the Rhombus by making ES and ST parallel to BT and EB respectively of length 6 cm each.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area = 

Question 3.

Draw rhombus BEST with the following measurements and calculate its area.

BE = 6 cm and ∠B = 45°.

Answer:

Step 1 – Draw a line BE of length 6 cm.

Step 2 – Draw a line at an angle 45° from point B and make a circle of radius 6 cm centered at E, the point of intersection of this line and this circle gives us the point S.

Step 4 – Complete the Rhombus by making BT and ST parallel to SE and BE.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area = 

Question 4.

Draw rhombus BEST with the following measurements and calculate its area.

BE = 7.5 cm and ∠E = 65°.

Answer:

Step 1 – Draw a line BE of length 7.5 cm.

Step 2 – Draw a line at an angle 65° from E and circle of radius 7.5 cm centered at E, the intersection of this line and circle gives the point S.

Step 4 – Complete the Rhombus by making BT and ST parallel to BE and SE respectively.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area = 

Question 5.

Draw rhombus BEST with the following measurements and calculate its area.

BS = 10 cm and ET = 8 cm.

Answer:

Diagonals of a Rhombus bisect each other at Right Angle.

Step 1 – Draw a line BS of length 10 cm and a line ET of length 8 cm which is a perpendicular bisector of line BS.

Step 2 – Join the four points to make the Rhombus.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area = 

Question 6.

Draw rhombus BEST with the following measurements and calculate its area.

BS = 6.8 cm and ET = 8.4 cm.

Answer:

Diagonals of a Rhombus bisect each other at Right Angle.

Step 1 – Draw a line BS of length 10 cm and a line ET of length 8 cm which is a perpendicular bisector of line BS.

Step 2 – Join the four points to make the Rhombus.

Question 7.

Draw rhombus BEST with the following measurements and calculate its area.

BS = 10 cm and ∠B = 60°.

Answer:

BS is a diagonal

Step 1 – Draw a line BS of length 10 cm.

BS is an angle bisector of ∠B as it is a diagonal in the Rhombus.

Also, opposite angles of a Rhombus are equal.

Step 2 – Draw lines at an angle 30° from B and S.

Here, ∠B = ∠S = 60°

∴ they make 30° with the diagonal BS as it is an angle bisector in a Rhombus.

Step 3 – Mark the intersecting points as E and T to complete the Rhombus.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area = 

Question 8.

Draw rhombus BEST with the following measurements and calculate its area.

ET = 9 cm and ∠E = 70°.

Answer:

ET is a diagonal

Step 1 – Draw a line ET of length 9 cm.

ET is an angle bisector of ∠E as it is a diagonal in the Rhombus.

Also, opposite angles of a Rhombus are equal.

Step 2 – Draw lines at an angle 35° from E and T.

Here, ∠E = ∠T = 70°

∴ they make 35° with the diagonal ET as it is an angle bisector in a Rhombus.

Step 3 – Mark the intersecting points as B and S to complete the Rhombus.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area = 

---

Exercise 2.2

Question 1.

Construct rectangle JUMP with the following measurements. Find its area also.

JU = 5.4 cm and UM = 4.7 cm.

Answer:

Step 1 – Construct a line JU of length 5.4 cm

Step 2 – Construct a line UM of length 4.7 cm perpendicular to the line JU.

Step 3 – Complete the rectangle by making JP and PM perpendicular to JU and UM respectively.

Area = length × breadth

A = 5.4 × 4.7

A = 25.38 cm²

Question 2.

Construct rectangle JUMP with the following measurements. Find its area also.

JU = 6 cm and JP = 5 cm.

Answer:

Step 1 – Construct a line JU of length 6 cm

Step 2 – Construct a line JP of length 5 cm perpendicular to the line JU.

Step 3 – Complete the rectangle by making UM and PM perpendicular to JU and JP respectively.

Area = length × breadth

A = 5 × 6

A = 30 cm²

Question 3.

Construct rectangle JUMP with the following measurements. Find its area also.

JP = 4.2 cm and MP= 2.8 cm.

Answer:

Step 1 – Construct a line JP of length 4.2 cm

Step 2 – Construct a line MP of length 2.8 cm perpendicular to the line JP.

Step 3 – Complete the rectangle by making JU and MU perpendicular to JP and MP respectively.

Area = length × breadth

A = 2.8 × 4.2

A = 11.76 cm²

Question 4.

Construct rectangle JUMP with the following measurements. Find its area also.

UM = 3.6 cm and MP = 4.6 cm.

Answer:

Step 1 – Construct a line MP of length 4.6 cm

Step 2 – Construct a line UM of length 3.6 cm perpendicular to the line MP.

Step 3 – Complete the rectangle by making JP and UJ perpendicular to MP and UM respectively.

Area = length × breadth

A = 3.6 × 4.6

A = 16.56 cm²

Question 5.

Construct rectangle MORE with the following measurements. Find its area also.

MO = 5 cm and diagonal MR = 6.5 cm.

Answer:

Step 1 – Construct a line MO = 5 cm

Step 2 – Draw a ray perpendicular to MO passing through O

Step 3 – Cut an arc of length 6.5 cm on the ray with M as center and mark the intersecting point as R.

Step 4 – Complete the rectangle by making RO and MO perpendicular to RE and ME respectively.

Measure RE

⇒ RE = 4.2 cm

Area = 5 × 4.2

Area = 21

Question 6.

Construct rectangle MORE with the following measurements. Find its area also.

MO = 4.6 cm and diagonal OE = 5.4 cm.

Answer:

Step 1 – Construct a line MO = 4.6 cm

Step 2 – Draw a ray perpendicular to MO passing through M

Step 3 – Cut an arc of length 5.4 cm on the ray with O as center and mark the intersecting point as E.

Step 4 – Complete the rectangle RE and EO perpendicular to MR and MO respectively.

Measure OE

⇒ OE = 2.8 cm

Area = 4.6 × 2.8

Area = 12.88 cm²

Question 7.

Construct rectangle MORE with the following measurements. Find its area also.

OR = 3 cm and diagonal MR = 5 cm.

Answer:

Step 1 – Construct a line OR = 3 cm

Step 2 – Draw a ray perpendicular to OR passing through O

Step 3 – Cut an arc of length 5 cm on the ray with R as center and mark the intersecting point as M.

Step 4 – Complete the rectangle ME and RE perpendicular to MO and OR respectively.

Measure RE

⇒ RE = 4 cm

Area = 3 × 4

Area = 12 cm²

Question 8.

Construct rectangle MORE with the following measurements. Find its area also.

ME = 4 cm and diagonal OE = 6 cm.

Answer:

Step 1 – Construct a line OR = 3 cm

Step 2 – Draw a ray perpendicular to ME passing through M

Step 3 – Cut an arc of length 6 cm on the ray with E as center and mark the intersecting point as O.

Step 4 – Complete the rectangle OR and RE perpendicular to MO and ME respectively.

Measure RE

⇒ RE = 5.2 cm

Area = 3 × 5.2

Area = 15.6 cm²

Question 9.

Construct square EASY with the following measurements. Find its area also.

Side 5.1 cm.

Answer:

Step 1 – Construct a line EA of length 5.1 cm.

Step 2 – Draw lines AS and EY perpendicular to EA of length of EA.

Step 3 – Join S and Y

Area of Square = side × side = side²

Area = 5.1² = 26.01 cm²

Question 10.

Construct square EASY with the following measurements. Find its area also.

Side 3.8 cm.

Answer:

Step 1 – Construct a line EA of length 3.8 cm.

Step 2 – Draw lines AS and EY perpendicular to EA of length of EA.

Step 3 – Join S and Y

Area of Square = side × side = side²

Area = 3.8² = 14.44 cm²

Question 11.

Construct square EASY with the following measurements. Find its area also.

Side 6 cm.

Answer:

Step 1 – Construct a line EA of length 6 cm.

Step 2 – Draw lines AS and EY perpendicular to EA of length of EA.

Step 3 – Join S and Y

Area of Square = side × side = side²

Area = 6² = 36 cm²

Question 12.

Construct square EASY with the following measurements. Find its area also.

Side 4.5 cm.

Answer:

Step 1 – Construct a line EA of length 4.5 cm.

Step 2 – Draw lines AS and EY perpendicular to EA of length of EA.

Step 3 – Join S and Y

Area of Square = side × side = side²

Area = 4.5² = 20.25 cm²

Question 13.

Construct square GOLD, one of whose diagonal is given below. Find its area also.

4.8 cm.

Answer:

Step 1 – Draw a line GL of length 4.8 cm

Step 2 – Draw a perpendicular bisector DO of GL of same length as GL

HERE GL = DO = 4.8 cm

Step 3 – Join the four points GOLD

Area of square =  (where D is the Diagonal)

Area = 

Area = 11.52 cm²

Question 14.

Construct square GOLD, one of whose diagonal is given below. Find its area also.

3.7 cm.

Answer:

Step 1 – Draw a line GL of length 3.7 cm

Step 2 – Draw a perpendicular bisector DO of GL of same length as GL

HERE GL = DO = 3.7 cm

Step 3 – Join the four points GOLD

Area of square =  (where D is the Diagonal)

Area = 

Area = 6.845 cm²

Question 15.

Construct square GOLD, one of whose diagonal is given below. Find its area also.

5 cm.

Answer:

Step 1 – Draw a line GL of length 5 cm

Step 2 – Draw a perpendicular bisector DO of GL of same length as GL

HERE GL = DO = 5 cm

Step 3 – Join the four points GOLD

Area of square =  (where D is the Diagonal)

Area = 

Area = 12.5 cm²

Question 16.

Construct square GOLD, one of whose diagonal is given below. Find its area also.

7 cm.

Answer:

Step 1 – Draw a line GL of length 7 cm

Step 2 – Draw a perpendicular bisector DO of GL of same length as GL

HERE GL = DO = 7 cm

Step 3 – Join the four points GOLD

Area of square =  (where D is the Diagonal)

Area = 

Area = 24.5 cm²