what is the area of a trapezoid with a height 5m and bases 8m and 1m? 6.5m². 22.5m². 24m². 45m²
The area of a trapezoid is found by multiplying the height by the sum of the lengths of the bases and dividing the result by 2.
Using this formula, the area of the trapezoid with a height of 5m, base lengths of 8m and 1m would be:
Area = (8 + 1) * 5 / 2 = 9 * 5 / 2 = 45 / 2 = 22.5m²
Therefore, the correct answer is 22.5m².
A trapezoid has an area of 166.5in², a height of 9in², and one base measuring 15in² what is the length of the other bases
Let's denote the length of the other base as "x".
The formula for the area of a trapezoid is A = (1/2)(b1 + b2)(h), where b1 and b2 are the lengths of the bases and h is the height.
We can substitute the given values into the formula:
166.5 = (1/2)(15 + x)(9)
Multiply both sides by 2 to eliminate the fraction:
333 = (15 + x) * 9
Divide both sides by 9:
37 = 15 + x
Subtract 15 from both sides:
x = 37 - 15
x = 22
Therefore, the length of the other base is 22 inches.
a regular pentagon has an apothem of 3.2m and an area of 37.2m² what is the length of one side of the pentagon
To find the length of one side of a regular pentagon, we can use the formula:
Area = (1/2) × apothem × perimeter
Given the apothem as 3.2m and the area as 37.2m², we can solve for the perimeter:
37.2 = (1/2) × 3.2 × perimeter
Multiply both sides by 2 and divide by 3.2:
37.2 × 2 / 3.2 = perimeter
Perimeter = 23.25
Since a regular pentagon has five equal sides, we can divide the perimeter by 5 to find the length of one side:
23.25 / 5 = 4.65
Therefore, the length of one side of the pentagon is approximately 4.65m.
if there is a dot in the center of the square and a line from the dot to one of the corners of the square and it is 12 cm what is the area of the square
To find the area of the square, we need to know the length of one side.
From the given information, we know that there is a line from the dot in the center of the square to one of the corners, and it measures 12 cm. This line is actually the diagonal of the square.
In a square, the diagonal divides the square into two congruent right triangles. And since the diagonal divides the square into two right triangles, each with one side equal to the half of the side of the square, we can apply the Pythagorean theorem to find the length of one side of the square.
Let's denote the length of one side of the square as "s".
Using the Pythagorean theorem:
s² + s² = 12²
2s² = 144
s² = 72
s ≈ √72
s ≈ 8.49 cm
Therefore, the length of one side of the square is approximately 8.49 cm.
Now, we can calculate the area of the square:
Area = s² = (8.49 cm)² = 72.08 cm²
Therefore, the area of the square is approximately 72.08 cm².
a regular hexagon has perimeter 60in what is the hexagon's area
To find the area of a regular hexagon, we need to know the length of one side of the hexagon.
Since a regular hexagon has six equal sides, we can divide the perimeter by 6 to find the length of one side:
Length of one side = Perimeter / 6 = 60in / 6 = 10in.
To find the area of the regular hexagon, we can use the formula:
Area = (3 * √3 * s²) / 2,
where s is the length of one side of the hexagon.
Using the length of one side as 10in:
Area = (3 * √3 * (10in)²) / 2
Area = (3 * √3 * 100in²) / 2
Area = (300 * √3) / 2
Area = 150 * √3
Therefore, the area of the regular hexagon is 150 * √3 square inches.