Kevin S. answered • 03/30/20
A math geek who loves helping others
Hi!
The area of a trapezoid is height * (base 1 + base 2)/2 = 10 * (15+21)/2 = 10* 36/2 = 10*18 = 180
For perimeter, we know the length of two sides (the bases) but not the slanted sides. That's no problem for us!
We know that base 1 is 7 units shorter than base 2. Base 2 has 7 units split between the two edges that extend past base 1, giving each extended leg a measure of 3.5 units. Now we have two right triangles with sides 10 and 3.5 with an unknown hypotenuse.
Using the Pythagorean theorem,
x^2 = 3.5^2 +10^2 = 10.24 +100 = 110.24
We take the square root of both sides to get x = 10.5
Perimeter means we add up all the sides of the shape : 21 + 15 + 10.5 + 10.5 = 57 units
Happy mathing!
Anthony M.
Hi! I'm sorry for down voting! I just want to point out an error. Base 1 is 6 units shorter than base 2. Therefore, if we are to assume the trapezoid is symmetrical, the two edges of base 2 that extend past base 1 are both 3 units. Our right triangles will have legs that are 10 units and 3 units. You can do the rest of the math from here using the Pythagorean Theorem. Kevin does a great job pointing out the steps. Thanks!03/31/20