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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)

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step-by-step explanation: