найдите площадь прямоугольной трапеции,большая бок - Троечка.com
Опубликовано 2 года назад по предмету Геометрия от Гость

найдите площадь прямоугольной трапеции,большая боковая сторона которого 6√2 см,острый угол 45° и меньшее основание 4 см.

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Опустим высоту CH на основание AD

ΔCHD - прямоугольный и ∠CDH = 45° ⇒ и ∠DCH = 45° и он равнобедренный. Найдем:

[tex]CH=HD=CD*\sin{45\dot{}}=6\sqrt{2}*\frac{1}{\sqrt{2}}=6[/tex]

Найдем площадь трапеции:

[tex]S=\frac{AD+BC}{2}*CH=\frac{AH+HD+BC}{2}*CH=\frac{HD+2*BC}{2}*CH=\frac{6+2*4}{2}*6=42[/tex]

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Здравствуй!

ΔСРД: ∠Д=45° ⇒ ∠С=45° ⇒ ΔСРД - равнобедренный и прямоугольный. Найдем стороны СР=РД по теореме Пифагора: пусть СР=РД=х см

[tex]x^{2} +x^{2} =(6\sqrt{2} )^{2} \\x=6[/tex]

СР=РД=6 см

ВС=АР=4 см

Sтрапеции=[tex]\frac{10+4}{2} *6=42 \ cm^{2}[/tex]

Ответ: 42 см²

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