An isosceles trapezoid has bases of length 20 and 12 centimeters and legs of length 11 centimeters what is the area of the trapezoid to the nearest tenth
To find the area of an isosceles trapezoid, you can use the formula:
Area = [(sum of the bases) / 2] * height
In this case, the bases of the trapezoid are 20 and 12 centimeters, and the legs are 11 centimeters. Since it is an isosceles trapezoid, we can calculate the height using the Pythagorean theorem.
Let's denote the height of the trapezoid as 'h' and the length of the leg as 'a'. Since the trapezoid is isosceles, we can divide it into two right-angled triangles.
Using the Pythagorean theorem, we can find the height 'h':
h = √(a^2 - [(b2 - b1) / 2]^2)
In our case, 'a' is the leg length, which is 11 cm. 'b1' and 'b2' are the lengths of the bases, which are 20 cm and 12 cm, respectively.
h = √(11^2 - [(20 - 12) / 2]^2)
h = √(121 - [(8) / 2]^2)
h = √(121 - [4]^2)
h = √(121 - 16)
h = √105
h ≈ 10.246 cm (rounded to three decimal places)
Now that we have the height, we can calculate the area using the formula mentioned earlier:
Area = [(sum of the bases) / 2] * height
Area = [(20 + 12) / 2] * 10.246
Area = (32 / 2) * 10.246
Area = 16 * 10.246
Area ≈ 162.74 cm² (rounded to two decimal places)
Therefore, the area of the trapezoid, to the nearest tenth, is approximately 162.7 square centimeters.