Answer:
OC = 16.7 cm
OAB = 332.9 cm² (1d.p)
OABD = 589.9 cm²(1d.p)
ABD = 257.1 cm²
Step-by-step explanation:
It is given that OC is 90° perpendicular to the line AB. In order to find OC, you can use Trigonmoetric formula, cosθ = adj./hypo. :
cosθ = adj./hypo.
adj. = OC cm
hypo. = 26 cm
θ = 100° ÷ 2
= 50°
cos 50 = OC/26
OC = 26 cos 50
= 16.7 cm (1d.p)
Next, is to find the area of triangle OAB using A = (1/2)×a×b×sinc :
a = 26 cm
b = 26 cm
c = 100°
A = (1/2)×26×26×sin 100
=332.87 cm² (2d.p)
Then, find the area of sector OABD using A = (θ/360)×π×r² :
θ = 100°
r = 26 cm
A = (100/360)×π×26²
= 589.92 cm² (2d.p)
Lastly, to find the area of segment ABD, you can to substract the area of triangle from the area of sector :
A = 589.92 - 332.87
= 257.1 cm² (1d.p)
