Answer:
The perimeter is 28.13 cm
Step-by-step explanation:
We connect a line from A to C
we can use the cosine rule to find the length AC
let us call it x
AC^2 = AB^2 + BC^2 - 2(AB)(BC) cos B
we have this as;
x^2 = 6^2 + 8^2 - 2(6)(8) cos 95
x^2 = 36 + 64 + 8.37
x^2 = 108.37
x = √108.37
x = 10.4 cm
AC = 10.4 cm
now, let us look at triangle ADC Where we have AC as the hypotenuse as it is the side facing the right angle
We can use Pythagoras’ theorem to get the value of CD
We have it that the square of the hypotenuse AC is the sum of the squares of the two other sides
let DC be y
10.4^2 = 5^2 + y^2
y^2 = 108.37 - 25
y^2 = 83.37
y = √83.37
y = 9.13 cm
The perimeter of the shape is the sum of all its sides
so we have;
AB + BC + CD + AD
= 6 + 8 + 9.13 + 5
= 28.13 cm