Question

WHAT IS THE AREA OF THE ADJOINING FIGURE ??

Answer 1

Answer:

90 square units

Step-by-step explanation:

In order to figure out the Area of the shape ABCDEFG, let's draw the rectangle ABHDEIFG by extending line segment AB up to H, so that, HDE becomes single straight line.  Similarly, extending line segment DE up to I, so that IFG becomes single straight line.

Now in the rectangle AHIG, Length is HI = AG = 16.

And breadth AH = AB + BH = AB + CD  [∵ BHDC is another rectangle, where BH = CD = 5  and HD = BC = 4]

∴ AH = AB + CD = 3 + 5 = 8 . . . . . . . . . . . (i)

∴ Area of rectangle AHIG = AG x ABH = 16 x 8 = 128

Area of the shape ABCDEFG = Area of rectangle AHIG - Area of rectangle BHDC - Area of Right Triangle EIF

= 128 - 4 x 5 - $\frac{1}{2}$EI.IF = 128 - 20 - $\frac{1}{2}$(AG - BC - DE)(AH - FG)

= 108 - $\frac{1}{2}$(16 - 4 - 6)(8 - 2)  [putting the value of AH from equation (i)]

= 108 - 18 = 90 square units