Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

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
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.