The sides of two similar hexagons are in a ratio of 3:7. The area of the smaller hexagon is 36in2. Find the area of the larger hexagon.

The area of the larger hexagon is 196 in²

Step-by-step explanation:

Area of a regular hexagon is given as;

where;

a is side of the hexagon

Given the area of the smaller hexagon as 36in², we now determine the side of this smaller hexagon.

A = (2.59808)a²

a² = A /  (2.59808)

a² = 36in² / (2.59808)

a² = 13.8564 in²

a = √ 13.8564 in²

a = 3.7224 in

let the side of the larger hexagon = b

Given the ratio of the sides of  small to large hexagon as 3:7,

a:b = 3:7

Now, with the side of the larger hexagon known, we calculate its area.

A = (2.59808)b²

A = (2.59808)(8.6856)²

A = 196 in²

Therefore, the area of the larger hexagon is 196 in²

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step-by-step explanation: