A New Square Is Formed By Joining The Midpoints Of The Consecutive Sides Of A Square 8 Inches On A Side. If The Process Is Continued Until There Are A

A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a side. If the process is continued until there are already six squares, find the sum of the areas of all squares in square inches.

a. 96
b. 112
c. 124
d. 126

 

Area of the Square:

The sum of the areas of all six squares formed by joining the midpoints of the consecutive sides of a square 8 inches on a side in square inches is 126.

Given: square 1 – 8 inches per side

Solution:

  1. Solve for the area of the first square using the formula A = s² such that,  A = (8 inches)² = 64 inches².  Therefore, area of the first square is 64 inches².
  2. Given that the next square is formed by connecting the midpoints of the first square then we can get the area of the second square by dividing the area of the first square by 2 which is 64/2 = 32. Thus, the area of the second square is 32 inches².
  3. Get the area of the third square by dividing the area of the second square by 2 which is 32/2 = 16. Thus, the area of the third square is 16 inches².
  4. Get the area of the fourth square by dividing the area of the third square by 2 which is 16/2 = 8. Thus, the area of the fourth square is 8 inches².
  5. Get the area of the fifth square by dividing the area of the fourth square by 2 which is 8/2 = 4. Thus, the area of the fifth square is 4 inches².
  6. Get the area of the sixth square by dividing the area of the fifth square by 2 which is 4/2 = 2. Thus, the area of the sixth square is 2 inches².
  7. Find the sum of all the areas from the first square to the sixth square thus, 64 + 32 + 16 + 8 + 4 + 2 = 96 +24 + 6 = 96 + 30 = 126 inches².
  8. Therefore, the sum of all the squares from the first to the sixth square is 126 inches².

Code: 10.3.1.1

For more information regarding areas of the square, go to the following links:

brainly.ph/question/98935

brainly.ph/question/1608395

brainly.ph/question/104736


Comments

Post a Comment

Popular posts from this blog

Ang Wika Ay Nag Iingat Ng Kasaysayan. Ipaliwanag

Ang wika ay nag iingat ng kasaysayan. Ipaliwanag   Answer: Ang wika ang sumisimbolo ng kakayahang nagpabago sa atin ngayon dahil ang wika ay isang patunay ng kasasayan noon na ibig sabihin ay nalampasan natin ang parusa at paghihirap na dinanas nang ating ninuno para sa lamang sa ating henerasyon, kaya ginagamit natin ito (wika) bilang pagbibigay ng karangalan at respeto sa kabayananihan na ginawa nila sa ating bansa at magsisilbing patunay na ang wika natin ay siyang bunga ng ating kasaysayan. (This all statement are based on me, kaya sana po ay hindi niyo ikinagagalit ang aking opinyon. Sagot ko po ito base sa tanong, maraming salamat po.) Explanation:
Read more

This Passage Would Most Probably Interest A/An __________.A. Adolescent B. Adult C. Child D. Old Man

This passage would most probably interest a/an __________.a. adolescent b. adult c. child d. old man   Overcome an Obstacle to Succeed by: Eddie Harris This passage would most probably interest a/an adolescent.   Explanation: The reason for choosing letter a or the adolescent is because the passage is about overcoming obstacle to succeed. Both the adult and the old man can no longer be advised on overcoming obstacle since they are almost at the full length of their ages and are considered having a lot of experiences in terms of overcoming obstacle and success . They are most likely to be interested in enjoying their lives and remaining days rather that overcoming obstacles and be successful since most old men are retirees and pensioners already and the adult is approaching just the same status. I did not choose also the child because it may refer to a new born or a toddler who is still innocent and will not be able to understand the principle of overcoming obstacle in order t
Read more