Question

Figure ABCD is a parallelogram. Points X and Y are placed so that BX ≅ DY and CD ⊥ XY.

The area of BXYC is 71.5 square units. What is the area of ABCD?

99 square units
110 square units
126 square units
143 square unit

Answer 1

Answer:

143 square units

Step-by-step explanation:

Given - BX=DY, CY =4 units, ar(BXYC) = 71.5 units²

We know that:

Opposite sides of a parallelogram are equal in length.

⇒ AB = CD

⇒ AX + BX = CY + DY

⇒ AX = CY = 4 units    (AX - CY = 0 because they are equal in length)  ----- (1)

and BX = DY  (given)  -------- (2)

From (1) & (2):

We can infer that XY divides the parallelogram ABCD into 2 trapeziums of equal areas.  {Length of Corresponding sides are equal and the height is common}

∴ Ar(ABCD) = 2.{ ar(BXYC) } = 2 (71.5) = 143 square units.

Hope you found my solution easy to understand.

Answer 2

Answer:

143 square unit

Step-by-step explanation:

ABCD is a parallelogram _ eq1

BX ≅ DY _ eq2

by eq(1,2)

so XY⊥ABCD

÷into two=part BXYC=ADYX

The area of BXYC is 71.5 square units

therefore 2×71.5 =143