Two similar hexagon have corresponding sides of 2cm and 5cm.find the ratio of their areas
Areas of similar shapes are proportional to the squares of their corresponding sides.
area-small : area-larger = 2^2 : 5^2 = 4:25
Well, if the sides of the two hexagons are in the ratio of 2cm to 5cm, then we can imagine them as two friends, let's call them Hexy and Gonny. Hexy has shorter sides while Gonny has longer sides. They sound like a hip hop duo!
Now, let's talk about the area. Areas are like dance floors - the bigger the area, the more space you have to groove. Since we're dealing with similar hexagons, the ratio of their areas will be the square of the ratio of their sides. So, if Hexy's sides are 2cm and Gonny's sides are 5cm, the ratio of their areas will be (2/5)².
Calculating that, we get:
(2/5)² = 4/25
So, the ratio of their areas is 4 to 25. It's like Hexy has 4 slices of pizza and Gonny has 25 slices of pizza. No wonder Gonny has more area to dance on!
Keep in mind that this is just a ratio, not the actual area. The actual areas will depend on the dimensions of the hexagons. But hey, at least now you know the ratio and can impress your friends with your geometric dance moves.
To find the ratio of the areas of two similar hexagons, we can use the fact that the ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.
Let's assume the area of the first hexagon is A1 and the area of the second hexagon is A2.
Given that the corresponding sides of the hexagons are 2 cm and 5 cm, we can set up the following proportion:
2 cm / 5 cm = √(A1 / A2)
Now, let's solve for the ratio of the areas:
(2 cm / 5 cm)^2 = A1 / A2
(2/5)^2 = A1 / A2
4/25 = A1 / A2
Therefore, the ratio of the areas A1/A2 is 4/25.
To find the ratio of the areas of two similar hexagons, we need to know the relationship between their corresponding side lengths.
In this case, we are given that the corresponding sides of the hexagons are 2 cm and 5 cm.
The area of a regular hexagon can be calculated using the formula:
Area = (3√3/2) * s^2
Where s is the length of a side of the hexagon.
Let's calculate the area of the first hexagon:
Area1 = (3√3/2) * (2 cm)^2 = (3√3/2) * 4 cm^2 = 6√3 cm^2
Now, let's calculate the area of the second hexagon:
Area2 = (3√3/2) * (5 cm)^2 = (3√3/2) * 25 cm^2 = 75/2 * √3 cm^2
To find the ratio of their areas, we can divide the area of the second hexagon by the area of the first hexagon:
Ratio = Area2 / Area1 = (75/2 * √3 cm^2) / (6√3 cm^2)
Now, we can simplify the expression:
Ratio = (75/2 * √3 cm^2) / (6√3 cm^2)
= 25/4
Therefore, the ratio of the areas of the two similar hexagons is 25/4.