Question

Proszę o zrobienie zadań 2-5 ze zdj

Answer 1

Zad1)
α + 110⁰ =180⁰
α = 180⁰ -110⁰ =70⁰
α + β =180⁰ ;  70⁰ + β = 180⁰ ,  β = 180⁰ - 70⁰ = 110⁰
γ + 93⁰ =180°  ; γ = 180⁰ -93⁰ = 87⁰

Zad2)
Obw = a + b + 2c;
a,b -dł. podstaw  trapezu
c- dł. ramion trapezu
Obw = 200cm
a / b = 1/4
b= 4a
W czworokącie , opisanym na  okręgu , sumy  długości przeciwległych boków ,są  równe.

a+ b = c+c
a+b = 2c
a + 4a = 2c
5a =2c /:2
c= 5a/2
 200 = a + b +2c
200 = a +4a + 2 x 5a/2
200 = 5a + 5a
200 =10a /:10
a = 10 cm
b= 4a = 4 x 10 cm =40 cm
c= 5a/2 = 5 x 10 cm /2 = 50 cm /2 =25cm
Zad3)
Obw ABCD = 20cm;
 Obw A' B' C' D' = 2 x 2cm + 2 x 5cm = 4cm + 10cm = 14cm ;

a,b -dł. boków prostokąta  ABCD , a < b
20 = 2a +2b
20 = 2( a+b) /:2
10 = a+b
b= 10 -a
 
2/ 4 = a/b
2b = 4a
2 ( 10 -a) =4a
20 - 2a =4a
6a = 20/:6
a = 20/6 = 3 i 2/6 = 3 i 1/3
b = 10 - 3 i 1/3 = 6 i 2/3
P ABCD = a x b = 3 i 1/3  x 6 i 2/3  = 10/3 x 20/3 = 200/9 = 22 i 2/9 cm²

Zad4)
k II l II m
Korzystam z  tw. Talesa
8/y = 8 + 6 /10
8 / y = 14 / 10
14y = 80 /: 14
y = 80/14 = 40 / 7 = 5 i 5/7

x/y = x +5 /10
x / 40/7  = x +5 /10
10x = 40/7 x (x+5)
10x = 40/7x + 200/7 /x 7
70x = 40x + 200 /- 40x
30x =200 / : 30
x = 20/3  = 6  i  2/3

z/12 = x / 8
8z = 12x /:8
z = 12/8 x  = 12/8 x 20/3 = 3/2 x 20/3 = 10
Zad5)
IABI =6
ICDI =4

IADI =3

3/6 = 2/ x
3x = 12 /: 3
x = 4
3/4 = 2 / y
3y = 8 /3
y =8/3 = 2 i 2/3
P(ABCD) = 1/2 x ( IABI + ICDI) x IADI  = 1/2 x ( 6 + 4) x 3 = 1/2 x 10 x 3 = 5 x 3 = 15 cm ² ; pole  trapezu  ABCD
 Pole niezakreskowanego  trapezu  = 1/2 x ( 4 + 8/3 ) x 2 = 1/2 x(12/3 + 8/3) x 2 = 20/3 = 6 i 2/3 cm²

Pole  zakreskowanej  figury = 15 cm² - 6 i 2/3cm² = 15 - 20/3 = 45/3 - 20/3 = 25/3  = 8 i 1/3 cm²