Two similar hexagons have corresponding sides of 2cm and 5cm
a) find the ratio of their areas
b)the area of the larger hexagon is 150 cm square
Find the area of the smaller one
smaller area : larger area = 2^2 : 5^2 = 4 : 25
smaller : 150 = 4 : 25
smaller hexagon = 4/25(150) = 24 cm^2
Find ratio of their angles is 2/5
So 2/5=4/25=
150*25/4=937.5
1+2÷2<1÷4
To solve this problem, we'll use the fact that the ratio of the areas of two similar polygons is equal to the square of the ratio of their corresponding side lengths.
a) Ratio of areas:
We have two similar hexagons with corresponding side lengths of 2 cm and 5 cm. The ratio of their side lengths is 5/2.
Let's calculate the ratio of their areas:
Ratio = (5/2)^2
= 5^2 / 2^2
= 25 / 4
So the ratio of their areas is 25/4.
b) Finding the area of the smaller hexagon:
We are given that the area of the larger hexagon is 150 cm^2.
To find the area of the smaller hexagon, we'll use the ratio of their areas.
Let's set up the ratio:
Ratio = Area of larger hexagon / Area of smaller hexagon
= 150 / Area of smaller hexagon
Since we already know the ratio is 25/4, we can write:
25/4 = 150 / Area of smaller hexagon
Now, let's solve for the area of the smaller hexagon:
Area of smaller hexagon = (25/4) * (150)
= 3750 / 4
= 937.5 cm^2
So, the area of the smaller hexagon is 937.5 cm^2.
a) Ah, hexagons! They sound like the nerdy cousins of squares. Anyway, to find the ratio of their areas, we just need to square the ratio of their corresponding sides. So, the ratio of their areas is (5/2)^2, which is 25/4.
b) Alright, let's calculate the area of the smaller hexagon! Since we know the ratio of their areas is 25/4, and the area of the larger hexagon is 150 cm², we can set up a proportion. Let x be the area of the smaller hexagon, so we have (25/4) : 150 = 1 : x. Cross-multiplying, we get (25/4)*x = 150. Now, just solve for x and you'll have the answer!