30
14
27
First of all we work out the length of a sides ab, bc, CD, & ad. We know that ab = bc = CD = ad also ae = ac/2 If a to e = 2 then ac = 4 so ab2 + bc2 = ac2 2ab2 = 16 ab2 = 8 ab = 2.8284271247461900976033774484194 so the perimeter = ab * 4 = 11.31
Draw the isosceles trapezoid ABCE, where the length of the bases AB (on the top) and EC are respectively 10 and 20. From A and B draw the perpendiculars to the base EC of the trapezoid, and label the point of intersections with F and G). The rectangle ABGF is formed, where the length of FG is 10 (since the two opposite sides of a rectangle are congruent). Then the lengths of EF and GC are 5 (since the trapezoid is isosceles). Draw the diagonal AC. From C and E draw the parallel lines respectively to AE and AC, and label the intersection point with D. So the rectangle ACDE is formed. Thus, the triangle EAC is a right triangle, where the angle A is 90 degrees (as the angle of a rectangle), and AF is the altitude drawn at the hypotenuse EC. We have a theorem that states: "If an altitude is drawn to the hypotenuse of a right triangle, then each leg is the geometric mean between the hypotenuse and its touching segment on the hypotenuse". So we have, EC/AE = AE/EF, which yields AE2 = EC*EF, and so AE = √(20*5) = 10. or using the same diagram, Since the diagonals of a rectangle bisect each other (let's say they bisect at H), then AH is the median of the right triangle EAC, drawn to the hypotenuse EC, so its length is the half of the hypotenuse. So the length of AH is 10. Since the trapezoid is isosceles, then the diagonal BE also will form a right triangle EBC, where the median BH also it is 10. So the triangle ABH is equilateral, where angle A is 60 degrees, and it is congruent with angle H of the triangle AHE, as two alternate interior angles. Thus, the isosceles triangle AHE is also equilateral, where AE = 10.
30
24;
14
It is not possible to answer the question with the information provided. abcd is a polygon and, as such, cannot have a length. It is possible to say that ab = 2*af = 14 units and that, being the biggest dimension, is the length. However, the longest side is not always the length : sometimes the horizontal side is called the length with the vertical or angled side being the height.
27
8
AD,BC, and AE
First of all we work out the length of a sides ab, bc, CD, & ad. We know that ab = bc = CD = ad also ae = ac/2 If a to e = 2 then ac = 4 so ab2 + bc2 = ac2 2ab2 = 16 ab2 = 8 ab = 2.8284271247461900976033774484194 so the perimeter = ab * 4 = 11.31
There is not enough information provided in the question for it to be answerable.
A+=14 * * * * * Not sure what the above answer means. But whatever it is, it is not the correct answer to this question! ae is half of ad so the second figure has the linear dimensions of the second are half that of the first. Therefore, the perimeter is half ie 27 units.
Let's draw the parallelogram ABCD in which both pairs of opposite sides are parallel and congruent.From the vertices A and C draw the altitudes AE and CF respectively to the sides DC and AB of the parallelogram, which separates it into two congruent right triangles AED and CFB, and the rectangular AFCE. So that the area of the parallelogram equals to2(AAED) + AAFCE= 2[(DE x AE)/2] + (EC x AE)= (DE x AE) + (EC x AE)= (DE + EC)AE= DC x AE= base x heightThus, the area of any parallelogram equals to the product of its base and height.
Koichi Ae was born on 1976-04-15.