Question

В равнобедренной трапеции с основаниями 10 см и 22 см диагональ является биссектрисой острого угла трапеции.найти площадь трапеции

Answer 1

так как трапеция равнобедренная, то боковые стороны AB и CD трапеции равны между собой. Угол САВ= углу САД, так как АС – биссектриса угла ДАВ, угол ДАС=углу АСВ, как внутренние накрест лежащие при параллельных прямых СВ и АД, секущей АС. Следовательно треугольник СВА – равнобедренный, СВ=АВ=10. Из треугольника АВН, по теореме Пийфагора найдём ВН - высоту трапеции. ВН^2=АВ^2 – АН^2, АН=(АД – ВС):2=(22 – 10):2=6. ВН^2=10^2 – 6^2=100 – 36=64, ВН=8см. S=(BC+AD):2*BH=(10+22):2*8=16*8=128

Ответ: 128 

Answer 2

Finding the Area of an Isosceles Trapezoid

To find the area of the isosceles trapezoid, we can use the formula:

Area = (1/2) * (sum of the lengths of the parallel sides) * (height)

In this case, the trapezoid has bases of 10 cm and 22 cm, and the diagonal is the bisector of the acute angle of the trapezoid.

Calculation

The formula for the area of a trapezoid is given by:

Area = (1/2) * (a + b) * h

Where: - a and b are the lengths of the parallel sides (bases) - h is the height of the trapezoid

Given that the trapezoid has bases of 10 cm and 22 cm, and the diagonal is the bisector of the acute angle, we can use the properties of an isosceles trapezoid to find the height.

Using the Diagonal as the Bisector

In an isosceles trapezoid, the diagonals are equal, and the diagonal bisects the angles at the base. This means that the height of the trapezoid can be found using the Pythagorean theorem.

Let's denote the height of the trapezoid as h, and the legs of the trapezoid as a and b. Using the Pythagorean theorem, we have:

h^2 = (d^2 - (b - a)^2) / 4

Where: - d is the length of the diagonal - a and b are the lengths of the parallel sides (bases)

Substitute the Given Values

Substituting the given values: - d = 22 cm (length of the diagonal) - a = 10 cm (length of one base) - b = 22 cm (length of the other base)

We can calculate the height using the formula above.

Calculating the Area

Once we have the height, we can use the formula for the area of a trapezoid to find the area.

Let's calculate the height and then use it to find the area of the trapezoid.