(i) Using the dots of a grid as the vertices, can you create a square that has an area of (a) 2 sq. units, (b) 3 sq. units Class 8

(i) Using the dots of a grid as the vertices, can you create a square that has an area of (a) 2 sq. units, (b) 3 sq. units Class 8

Question 1.

(i) Using the dots of a grid as the vertices, can you create a square that has an area of (a) 2 sq. units, (b) 3 sq. units, (c) 4 sq.units, and (d) 5 sq. unit?

(ii) Suppose the grid extends indefinitely. What are the possible integer-valued areas of squares you can create in this manner? Class 8

Solution:

(a) Yes, in the grid area of ABCD is 2 sq. units.

(b) On the grid, it is not possible

(c) Yes, in the grid, area of PQRS = 4 sq. units.

(d) Yes, in the grid, it is not possible

(ii) Possible areas that can be created on the grid are 2 square units, 4 square units, 8 square units, 16 square units, 9 square units, 18 square units, 25 square units, 50 square units, etc.

Question 2.

Find the area of an equilateral triangle with sidelength 6 units. Class 8

[Hint : Show that an altitude bisects the opposite side. Use this to find the height.]

Solution:

Draw AD ⊥ BC.

So, ∆ABD ≅ ∆ACD (By RHS)

Hence, BD = DC = 3 cm

So, AD² = [latex]\sqrt{6^2-3^2}[/latex] = [latex]\sqrt{27}[/latex]

= [latex]3 \sqrt{3}[/latex] units

So, required area

= [latex]\frac{1}{2}[/latex] BC × AD

= [latex]\frac{1}{2}[/latex] × 6 × [latex]3 \sqrt{3}[/latex]

= [latex]9 \sqrt{3}[/latex] sq. units