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number of squares
figure 1 → 1 x (1 + 1) ÷ 2 = 1
figure 2 → 2 x (2 + 1) ÷ 2 = 2 x 3 ÷ 2 = 3
figure 3 → 3 x (3 + 1) ÷ 2 = 3 x 4 ÷ 2 = 6
let's say figure number is 1u
formula → 1u x (1u + 1) ÷ 2
465 = 1u x (1u + 1) ÷ 2
to remove ÷ 2 in an equation, we have to multply by 2
465 x 2 = 1u x (1u + 1) 930 = 1u x (1u + 1)
figure out what is 1u
easier way is to break them to easy numbers
930 = 900 + 30
so what multiple can you figure out from this
30 x 30 = 900
so lets try out 30 as 1u
1u x (1u + 1) ÷ 2 → 30 x (30 + 1) ÷ 2 = 465 squares
figure 30 → 30 x (30 + 1) ÷ 2 = 465 squares