alexphel
Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

On the following composite figure, all angles are right angles. All short edges of the figure have a measure of 1.5 centimeters. All long edges have a measure of 3 centimeters. Find the area of the figure. Explain or show how you got your answer.

people don't fail me now

On The Following Composite Figure All Angles Are Right Angles All Short Edges Of The Figure Have A Measure Of 15 Centimeters All Long Edges Have A Measure Of 3 class=

Sagot :

sqdancefan

Answer:

  27 cm²

Step-by-step explanation:

There are many ways the figure can be decomposed into parts for which you know the area formula. The total area is the sum of the parts.

__

decomposition

We recognize that each of the tabs is twice as long as wide, so is half a square. The 4 tabs together make 2 squares that are 3×3 cm. Of course, what remains after removing the tabs is a 3×3 cm square in the middle of the figure.

sum of parts

Then the total area is that of 3 squares measuring 3 cm × 3 cm:

  A = s² = (3 cm)² = 9 cm² . . . . . area of one square

  total area = 3A = 3(9 cm²) = 27 cm²

The area of the figure is 27 cm².

_____

Alternate solution

The figure can also be considered to be a 6 cm × 6 cm square with four 1.5 cm × 1.5 cm squares removed from its corners. Then the area is ...

  (6 cm)² -4(1.5 cm)² = (36 -4(2.25)) cm² = 27 cm²

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.