Find the altitude, perimeter and area of an isosceles trapezoid whose sides have lengths 10 cm, 20 cm , 10 cm, and 30 cm.
how??
make a sketch and draw an altitude (height) from the shorter side.
Now you have a right-angled triangle, use Pythagoras
ares of trapezoid = height (sum of parallel sides)/2
To find the altitude, perimeter, and area of an isosceles trapezoid, we can follow these steps:
1. Determine the height (altitude) of the trapezoid:
- Since an isosceles trapezoid has two parallel sides and two non-parallel sides, the height is the perpendicular distance between the two parallel bases.
- In this case, the bases are 20 cm and 30 cm, and we have two equal side lengths of 10 cm.
- To find the height, we can use the Pythagorean theorem. Let's label the height as 'h':
h² = 10² - ((30 - 20) / 2)²
Simplifying further:
h² = 100 - 25
h² = 75
h ≈ √75
h ≈ 8.66 cm (rounded to two decimal places)
2. Calculate the perimeter of the trapezoid:
- The perimeter is the total distance around the trapezoid.
- In this case, the sides have lengths of 10 cm, 20 cm, 10 cm, and 30 cm.
- To find the perimeter, we sum up the lengths of all four sides:
Perimeter = 10 cm + 20 cm + 10 cm + 30 cm
Perimeter = 70 cm
3. Determine the area of the trapezoid:
- The area of a trapezoid can be found using the formula: Area = ((a + b) / 2) * h, where 'a' and 'b' are the lengths of the parallel bases, and 'h' is the height (altitude).
- In this case, the lengths of the bases are 20 cm and 30 cm, and the height is approximately 8.66 cm.
- Plugging these values into the formula, we get:
Area = ((20 cm + 30 cm) / 2) * 8.66 cm
Area = (50 cm / 2) * 8.66 cm
Area = 25 cm * 8.66 cm
Area ≈ 216.5 cm² (rounded to one decimal place)
So, the altitude of the isosceles trapezoid is approximately 8.66 cm, the perimeter is 70 cm, and the area is approximately 216.5 cm².