ratio of sides = 5/2
ratio of areas = (5/2)^2 = 25/4
25/4 * 30 = 187.5
Small pentagon is 4m and the larger one is 10m
ratio of areas = (5/2)^2 = 25/4
25/4 * 30 = 187.5
Ratio of sides = 12/4 = 3
Therefore, the ratio of their areas is 3² = 9.
Area of larger pentagon = 9 * 30 = 270 m².
Ratio of sides = 10/8 = 5/4
Therefore, the ratio of perimeters is also 5/4, since perimeter is a linear function of the length of the sides.
The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides. In this case, the ratio of areas would be (10/8)² = 1.5625. So, the larger figure is approximately 1.5625 times the area of the smaller one.
A. perimeter 5/4 area 49/4
B. Perimeter 25/16 area 5/4
C. Perimeter 49/4 area 5/4
D. Perimeter 5/4 area 25/16
Ratio of perimeters = (perimeter of larger figure)/(perimeter of smaller figure) = (10+8+10+8+10)/(8+8+8+8+8) = 46/40 = 23/20
Ratio of areas = (area of larger figure)/(area of smaller figure) = (10*10)/(8*8) = 100/64 = 25/16
Therefore, the correct answer is:
D. Perimeter 5/4 area 25/16
A = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * a^2
where A is the area of the pentagon and a is the length of its side.
Substituting a = 5 in the formula, we get:
A = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * 25
Using a calculator to approximate the value, we get:
A ≈ 59.8
Rounding the answer to the nearest tenth, we get:
A ≈ 59.8 rounded to the nearest tenth is 59.8.
A. 7.75 m2
B. 64.25 m2
C. 85.64 m2
D. 92.99 m2
A = (θ/360) * πr^2
where A is the area of the sector, θ is the central angle of the sector in degrees, and r is the radius of the circle.
Substituting the given values, we get:
A = (74/360) * π * 12^2
Simplifying and using a calculator to approximate the value, we get:
A ≈ 85.64
Therefore, the area of the shaded sector is approximately 85.64 square meters.
Thus, the answer is option C. 85.64 m2.
12.9 in 9 in and 7.1 in right angle
A = b * h
where A is the area of the parallelogram, b is the length of its base, and h is its height.
In this case, the given base is 9 inches and the given height is 7.1 inches. So, we have:
A = 9 * 7.1
Multiplying these values, we get:
A = 63.9
Rounding the answer to the nearest tenth, we get:
A ≈ 63.9 rounded to the nearest tenth is 63.9.
Therefore, the area of the parallelogram is approximately 63.9 square inches.
A = √(s(s-a)(s-b)(s-c))
where A is the area of the triangle, a, b, and c are the side lengths, and s is the semi-perimeter (half of the perimeter) of the triangle, given by:
s = (a + b + c)/2
In this case, the given side lengths are a = 14 in, b = 37.2 in, and c = 29.5 in. So, we have:
s = (a + b + c)/2 = (14 + 37.2 + 29.5)/2 = 40.85
Substituting these values into Heron's formula, we get:
A = √(40.85(40.85-14)(40.85-37.2)(40.85-29.5))
Using a calculator to approximate the value, we get:
A ≈ 177.5
Rounding the answer to the nearest tenth, we get:
A ≈ 177.5 rounded to the nearest tenth is 177.5.
Therefore, the area of the triangle is approximately 177.5 square inches.