what is the area of a isosceles trapezoid with legs of 15 feet and bases of 10 feet and 28 feet?
Draw a symmetric trapezoid. Mark the center of the bases
On the long base, each side is covered by half the short base, of length 5. That leaves a triangle on each end that has base 9, hypotenuse 15.
Looks like a 3-4-5 triangle to me, with height 12.
area = (b+B)h/2 = (10+28)*12/2 = 228
Ah, an isosceles trapezoid! That's a shape that really knows how to stand out. To calculate its area, let's start by finding the average length of the bases. We have 10 feet and 28 feet, so that gives us an average of 19 feet. Now, the height of this trapezoid is not given, but let's pretend it's laughing at a really funny joke and stands tall at 8 feet.
Now, we can use the formula for finding the area of a trapezoid, which is 1/2 times the sum of the bases times the height. Plugging in the values, we get 1/2 times (10 feet + 28 feet) times 8 feet. Doing some math magic, this simplifies to 1/2 times 38 feet times 8 feet, which gives us an area of 152 square feet.
So, the area of this isosceles trapezoid with legs of 15 feet and bases of 10 feet and 28 feet is a whopping 152 square feet! That's big enough to host a clown party, don't you think?
To find the area of an isosceles trapezoid, you can use the formula:
Area = (1/2) * (a + b) * h
Where "a" and "b" are the lengths of the bases, and "h" is the height of the trapezoid.
In this case, the legs of the trapezoid are given as 15 feet, so the length of each leg is 15 feet. The bases are given as 10 feet and 28 feet.
To find the height of the trapezoid, you can use the Pythagorean theorem:
h = sqrt(l^2 - [(b - a)/2]^2)
Where "l" is the length of the leg, and "a" and "b" are the lengths of the bases.
For the first base of 10 feet:
h = sqrt(15^2 - [(10 - 15) / 2]^2)
= sqrt(225 - [(-5) / 2]^2)
= sqrt(225 - [(-2.5)^2])
= sqrt(225 - 6.25)
= sqrt(218.75)
≈ 14.8 feet
For the second base of 28 feet:
h = sqrt(15^2 - [(28 - 15) / 2]^2)
= sqrt(225 - [(13) / 2]^2)
= sqrt(225 - [(6.5)^2])
= sqrt(225 - 42.25)
= sqrt(182.75)
≈ 13.5 feet
Now that we have the height of the trapezoid, we can calculate the area using the formula:
Area = (1/2) * (10 + 28) * 13.5
= (1/2) * 38 * 13.5
≈ 256.5 square feet
Therefore, the area of the isosceles trapezoid is approximately 256.5 square feet.
To find the area of an isosceles trapezoid, you need to use the formula: A = (b1 + b2) * h / 2, where b1 and b2 are the lengths of the bases, and h is the height.
In this case, the shorter base (b1) is 10 feet, and the longer base (b2) is 28 feet. Since you haven't provided the height (h), we can't calculate the area directly.
To proceed, we need to find the height of the trapezoid. Fortunately, a helpful property of an isosceles trapezoid is that the height is equal to the length of the perpendicular segment drawn between the bases.
To find the height, we first need to determine the length of the top portion of the trapezoid, which is the difference between the longer base (28 feet) and the shorter base (10 feet). This gives us 28 - 10 = 18 feet.
Next, we divide the difference in lengths by 2 since we are dealing with an isosceles trapezoid. Therefore, the height (h) is 18 / 2 = 9 feet.
Now that we have the height, we can use the formula to compute the area: A = (b1 + b2) * h / 2. Plugging in the values we have: A = (10 + 28) * 9 / 2 = 38 * 9 / 2 = 342 / 2 = 171 square feet.
So, the area of the isosceles trapezoid with legs of 15 feet and bases of 10 feet and 28 feet is 171 square feet.