Question

Trapezul isoscel ABCD are Ab ||CD, AB =24cm. , CD=18 cm, iar m (unghiul A)=60 °. Determina:
A) Aria trapezului:
B) Lungimile diagonalelor trapezului
C) Distanta de la punctul C la dreapta AD

Answer 1

A)ducem DE_|_ AB
AE=(24-18):2=3
InΔDAE:
tg <A=DE/AE
√3=DE/3
DE=3√3
Aria ABCD=(AB+CD)*DE:2=(24+18)*3√3:2=63√3

b)DB=AC pt ca avem trapez isoscel
in ΔDEB:
EB=21
DB²=EB²+DE²=21²+(3√3)²=441+27=468
DB=6√13

c)fie CF_|_AD => CF=distanta de la C la AD
in ΔDAE, cos<A=AE/AD=> 
1/2=3/AD=> AD=6
in ΔDAC avem: 
Aria=CD*DE:2=AD*CF:2
18*3√3=6*CF
CF=9√3