Question

Авсд прямоугольная трапеция. ав=10, вс=10, угол сда= 45 градусов.найти ад и площадь авсд.Помогите пожалуйста)))

Answer 1

Разбиваем трапецию на квадрат со сторонами AB и BC. его площадь равна 100, и прямоугольный треугольник CDm, с высотой = AB = 10
Далее все просто. Т.к. угол CDA = 45, значит, треугольник - равнобедренный и mD = Cm = AB = 10. Значит:
Его площадь = 10*10 / 2 = 50
Расстояние AD = BC + mD = 20
Площадь всей трапеции = 100+50 = 150

Answer 2

Problem Statement

You are given a trapezoid ABCD, where AB = 10, BC = 10, and angle CDA = 45 degrees. You need to find the length of AD and the area of trapezoid ABCD.

Solution

To find the length of AD, we can use the fact that trapezoid ABCD is an isosceles trapezoid, meaning that the non-parallel sides are congruent. Therefore, AD = BC = 10.

To find the area of trapezoid ABCD, we can use the formula: Area = (sum of the lengths of the parallel sides) * (height) / 2.

In this case, the parallel sides are AB and CD, and the height is the perpendicular distance between AB and CD. Since trapezoid ABCD is isosceles, the height is the distance between AB and CD along the line passing through the midpoints of AB and CD.

Let's calculate the area step by step:

1. Find the length of the height: - Since trapezoid ABCD is isosceles, the height is the distance between AB and CD along the line passing through the midpoints of AB and CD. - The midpoint of AB is the point M, and the midpoint of CD is the point N. - The line passing through M and N is perpendicular to AB and CD. - The length of MN is half the sum of AB and CD: MN = (AB + CD) / 2 = (10 + 10) / 2 = 10. - Therefore, the length of the height is 10.

2. Calculate the area: - The sum of the lengths of the parallel sides is AB + CD = 10 + 10 = 20. - The height is 10. - Using the formula for the area of a trapezoid, we have: Area = (AB + CD) * height / 2 = 20 * 10 / 2 = 100.

Therefore, the length of AD is 10 units, and the area of trapezoid ABCD is 100 square units.

Please let me know if I can help you with anything else.