Question

An 'H' is cut from a 12'' * 12" square piece of paper. The area of th 'H' is __________ sq.in​

Answer 1

Area of H is 112 $cm^2$

Step-by-step explanation:

Let ABCD be the Square, where AB = BC = CD = DA = 12 cm

Area of Square is Square of Sides or $(Side)^2$

So Area of ABCD is $12 \times 12$  = 144 $cm^2$

• For an H to be constructed in a square,

Let us draw it as shown in the figure -  

• In the figure,  AKDG and LBCH along with MNIJ forms the Shape of H in Square ABCD.

• either we can sum up the areas of AKDG, LBCH, MNIJ or delete the areas of GHIJ and KLNM.

• where GHIJ & KLNM are Squares of side 4 cm each and  

AKDG with LBCH are rectangles with MNIJ as Square.

So, Area of Shaded Figure "H" is-

Area of ABCD - (Areas of Squares GHIJ and KLNM)

= 144 - $(4 \times 4 + 4 \times 4)$

= 144 - 32

= 112 $cm^2$