ABCD, BCEF, and BFGH are identical squares. (i) If the area of the red region is 49 sq. units Class 8

ABCD, BCEF, and BFGH are identical squares. (i) If the area of the red region is 49 sq. units Class 8

Question 1.

ABCD, BCEF, and BFGH are identical squares. Class 8

(i) If the area of the red region is 49 sq. units, then what is the area of the blue region?

(ii) In another version of this figure, if the total area enclosed by the blue and red regions is 180 sq. units, then what is the area of each square?

Solution:

Let side of each square is x units.

Then, area of ∆HDC = [latex]\frac{1}{2}[/latex] × x × 2x = x², which is the area of the red region.

So, x² = 49 or x = 7 units.

So, area of blue region

= Area of ∆ADP

=[latex]\frac{1}{2}[/latex] AD × AP

= [latex]\frac{1}{2}[/latex]x × [latex]\frac{x}{2}[/latex] (as AP = BP)

= [latex]\frac{x^2}{4}[/latex] = [latex]\frac{49}{4}[/latex]

= 12.25 sq. units.