From the diagram above, what is the area of the shaded parts?
We can take the squares roll by roll, starting from roll 1 (the topmost):
Roll 1: The total area of roll 1 is 4 unit sq. (1 sq. unit x 4), But the half of the area is not shaded so ¹⁄₂ x 4 sq, unit = 2 sq. unit And also the first square as the bottom half not shaded = ¹⁄₂ x 1 sq. unit = ¹⁄₂ sq. unit
So, shaded part of roll 1 is = 2 sq. unit - ¹⁄₂ sq. unit = 1¹⁄₂ sq. unit
Roll 2: We have a whole square and half of a square shaded = 1¹⁄₂ sq. unit
Roll 3: We have only half of a square shaded = ¹⁄₂ sq. unit
Total area shaded = 1¹⁄₂ +1¹⁄₂ + ¹⁄₂ = 3¹⁄₂ sq. unit
From the diagram above, what is the area of the shaded parts?
We can take the squares roll by roll, starting from roll 1 (the topmost):
Roll 1: The total area of roll 1 is 4 unit sq. (1 sq. unit x 4), But the half of the area is not shaded so ¹⁄₂ x 4 sq, unit = 2 sq. unit And also the first square as the bottom half not shaded = ¹⁄₂ x 1 sq. unit = ¹⁄₂ sq. unit
So, shaded part of roll 1 is = 2 sq. unit - ¹⁄₂ sq. unit = 1¹⁄₂ sq. unit
Roll 2: We have a whole square and half of a square shaded = 1¹⁄₂ sq. unit
Roll 3: We have only half of a square shaded = ¹⁄₂ sq. unit
Total area shaded = 1¹⁄₂ +1¹⁄₂ + ¹⁄₂ = 3¹⁄₂ sq. unit
Telegram has no known backdoors and, even though it is come in for criticism for using proprietary encryption methods instead of open-source ones, those have yet to be compromised. While no messaging app can guarantee a 100% impermeable defense against determined attackers, Telegram is vulnerabilities are few and either theoretical or based on spoof files fooling users into actively enabling an attack.
Mr. Durov launched Telegram in late 2013 with his brother, Nikolai, just months before he was pushed out of VK, the Russian social-media platform he founded. Mr. Durov pitched his new app—funded with the proceeds from the VK sale—less as a business than as a way for people to send messages while avoiding government surveillance and censorship.
