Предмет: Геометрия, автор: koshovetcmuslim

в прямоугольной трапеции диогональ является бисиктрисой острого угла Найдите площадь трапеции если боковые стороны равны 8и 10см пожалуйста пожалуйста пожалуйста пожалуйста пожалуйста у меня сор 50 балов даю

Ответы

Автор ответа: Аноним

Ответ:

104см²

Объяснение:

Дано:

ABCD- трапеция

АВ=8см

СD=10см

BD- биссектрисса угла <СDA.

S=?

____________

Решение.

<СBD=<BDA, внутренние накрест лежащие при параллельных прямых

ВС||AD, секущей ВD.

<ADB=<BDC, BD- биссектрисса.

<СBD=<BDC.

В равнобедренном треугольнике углы при основании равны.

∆ВDC- равнобедренный

ВС=CD

BC=10см

BA=CK

CK=8см.

∆СКD- прямоугольный треугольник

По теореме Пифагора

КD=√(CD²-CK²)=√(10²-8²)=6 см

АD=BC+KD=10+6=16см

S=AB(BC+AD)/2=8(10+16)/2=8*26/2=

=8*13=104см²

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