Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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 units

Sagot :

A quadrilateral in which opposite sides are parallel is called a parallelogram. The correct option is D.

What is a parallelogram?

A quadrilateral in which opposite sides are parallel is called a parallelogram. Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

For a parallelogram, the opposite sides are equal and parallel to each other. We can write,

AD ≅ BC

Since BX ≅ DY, therefore, we can write,

AB = CD

AX + XB = DY + YC

XB = DY, cancelling both the sides,

AX = YC.

Also, XY is the common side.

Since all the sides are equal also the angle are equal, therefore, it can be written,

AXDY ≅ CYXB

Given the area of CYXB is 71.5 square units. Therefore,

ABCD = CYXB + AXDY

ABCD = 2(CYXB)

ABCD = 143 square units.

Hence, the correct option is D.

Learn more about Parallelogram:

https://brainly.com/question/1563728

#SPJ1

View image ap8997154
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.