Question

Yellow parts have areas given in figure,.....
U have to find the area of Red part...​

Answer 1

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

• Area of a triangle = (1/2) × (Base × Height).
• Area of a parallelogram = (Base × Height).
• Two triangles on the same base (or equal bases) and between the same parallels are equal in area.
• In other words, area of a triangle is half the product of its base (or any side) and the corresponding altitude (or height).

From image we can see That :-

→ ∆EIB & ∆ADE are on same Base as AB, and between same parallel Lines AB & DC.

→ Both ∆'s have Same Height as Equal to the Height of ||gm.

So ,

→ Ar.[∆EIB] + Ar.[∆ADE]

→ (1/2 * EB * h) + (1/2 * AE * h)

→ (1/2 *h)[ EB + AE ]

→ (1/2 *h) * AB

→ (1/2)* (h * AB)

→ (1/2) * Area of llgm

Therefore ,

we can say That,

→ Ar.[∆EIB] + Ar.[∆ADE] = (1/2) * Area of llgm .

→ (72+d+8) + (x + b) = (1/2) * Area of llgm ------------ Equation (1) .

______________________

Now,

∆AFD is on Base AD and b/w Two parallel lines AD & BC..

So,

→ Ar.[AFD] = (1/2) * Area of llgm

→ (b + 79 + d + 10) = (1/2) * Area of llgm ----------------- Equation (2).

______________________

From Equation (1) & (2) now, we get,

→ (72+d+8) + (x + b) = (b + 79 + d + 10)

→ 80 + x + b + d = 89 + b + d

→ x + b + d - b - d = 89 - 80

→ x = 9 unit². (Ans).

Answer 2

We will use here :

1. Area of traingle. [Figure]
2. Area of parallelogram. [Figure]

Take set of triangles AED and EBG,

Area of ΔAED = x + a

Area of ΔEBG = 72 + b + 8

Concept :

Finding a triangle, or a set of triangles whose area is equal to 1/2 area of the parallelogram.

Now,

Total area of set of triangles = Area of parallelogram / 2

Substituting the values, we get,

x + a + 72 + b + 8 = Area of parallelogram / 2

Now taking ΔAFD,

Area of ΔAFD = a + 79 + b + 10 = Area of parallelogram / 2

Now,

x + a + 72 + b + 8 = a + 79 + b + 10

x = 79 + 10 - 72 - 8

x = 9 (Answer).