Find the areas of the following figures : Class 8

Find the areas of the following figures : Class 8

Question 1.

Find the areas of the following figures : Class 8

Solution:

(i) Area = [latex]\frac{1}{2}[/latex] (10 + 7) × 16 sq. ft.

= 136 sq. ft.

(ii) Area = [latex]\frac{1}{2}[/latex] (24 + 36) × 14 sq. m.

= 30 × 14 = 420 sq. m.

(iii) Area = [latex]\frac{1}{2}[/latex] (14 + 6) × 10 sq. in.

= [latex]\frac{20 \times 10}{2}[/latex] 100 sq. in.

(iv) Area = [latex]\frac{1}{2}[/latex](12 + 18) × 8 sq. ft.

= 15 × 8 sq. ft.

= 120 sq. ft.

Question 2.

[Sulba-Sutras] Give a method to convert an isosceles trapezium to a rectangle using dissection. Class 8

Solution:

Let ABCD be an isosceles trapezium, with AD = BC.

Draw AM ⊥ DC and BN ⊥ DC.

Cut ∆BNC and attach it to the other side of trapezium as shown in the figure.

That is C falls on A, N along BA and B falls on D.

Then, PBND is the required rectangle equal in area to the given trapezium.

Note : We can also cut ∆ADM and place on the other side of the trapezium for this purpose.