Find the area of the isosceles trapezoid. ( Use the Pythagorean Theorem.)?

Question

atrapezoid is drawn: the samller base is 7 cm, the height is 12 cm, the congruent legs are 13cm each.
my answer was 123.5 I am right?
and my second question is about a kite is drawn: the two smaller congruent side are 5cm the diagonal conecting the vertex point of the kit is cut by the smaller diagonal connecting the two nonvertex point the longer diagonal is broken into two parts that are 10 centimeters and 3 centimeters.
my answer is 80
please some help

Answer 1

If i've got the description right, you'll need to use Pyth. to find the missing leg of the congruent right triangles on each end of trap. formed by a height dropped. With a leg of 12 and a hypotenuse of 13, the missing leg must be 5. (This is one of the pythagorean triples you can memorize instead of using the theorem). So the longer base should be 5 on each end, plus the 7 that is identical to the smaller base. This gives us a base of 17(5 + 7 + 5) and the other base of 7, and a height of 12. Plug into the area formula of
A = 1/2(b1 + b2)h
A = 1/2(17 + 7)(12)
A = 1/2(24)(12)
A = 144 square centimeters.
I'm not sure where your answer came from, but you're not too far off.

2nd question, I'm assuming that you're looking for area again. On the side of the kite with 2 congruent right triangles with hypotenuse 5 and a leg of 3, those missing legs that are the pieces of the short diagonal must be 4 each. You've now got enough information to find the area. You've got two congruent triangles, formed by the longer diagonal of length 13. Each of these triangles should have a height of 4. Each triangle has an area of 1/2(13)(4) = 26, which means the total area of the kite is 52 square cm.

By the way, there is a shortcut for the area of a kite: A = 1/2 (diagonal 1)(diagonal 2).

Good luck with the rest of the geometry!

Answer 2

cut up the trapezoid into 3 areas, area a million= first outstanding triangle, part2 = rectangle, area 3 = 2nd rt trainagle portion of first outstanding triangle: A1 = base * top /2 as according to pythagorus theorem, c2 = a2 + b2, 169 = a hundred and forty four + b2 which factors b = 5 now portion of outstanding triange = 5 * 12/2 = 30 cm2 portion of 2nd triangle = portion of first triangle (isocelses trapeziod have cut up triangle as equivalent) portion of rectangle = 7 * 12 = 80 4 cm2 finished portion of trapezoid = 30 + 80 4 + 30 = a hundred and forty four cm2 wish this helps