abcd is trapezium bc is 17 ab is 16 dc is 8 find area of abcd
ABCD can be drawn with a right angle at A. Then, if you drop an altitude from CD to AB, it will divide AB into two equal parts of length 8.
Now on the right side you have a right triangle, with base=8 and hypotenuse=17. Now you can figure the height h, and so the area is
h * (8+16)/2
To find the area of trapezium ABCD, you can use the formula for the area of a trapezium, which is:
Area = (a + b) * h / 2
Where:
a and b are the lengths of the parallel sides of the trapezium
h is the height (perpendicular distance) between the parallel sides
In this case, the parallel sides are AB and DC, and the height is the perpendicular distance between them.
Given:
AB = 16
DC = 8
BC = 17
To find the height, we can use the Pythagorean Theorem. The height can be represented by the side AD.
Since ABCD is a trapezium, AB and DC are parallel. So, AD and BC are parallel as well, forming a parallelogram.
Using the Pythagorean theorem:
AD^2 = AB^2 - BD^2
Since AB = 16 and DC = 8, we can find BD by subtracting DC from AB since AB and BD are parallel sides of the trapezium.
BD = AB - DC
BD = 16 - 8
BD = 8
Substituting the values into the equation:
AD^2 = 16^2 - 8^2
AD^2 = 256 - 64
AD^2 = 192
Taking the square root of both sides:
AD = √192
AD = 13.86 (rounded to two decimal places)
Now that we have the height (AD) and the lengths of the parallel sides (AB and DC), we can substitute these values into the formula for the area of a trapezium:
Area = (AB + DC) * h / 2
Area = (16 + 8) * 13.86 / 2
Area = 24 * 13.86 / 2
Area = 332.64 / 2
Area = 166.32
Therefore, the area of trapezium ABCD is 166.32 square units.