Question

Please answer this it's confusing ​

Answer 1

K = 1710 cm^2 - K = 373.497 cm^2 = 1337 cm^2

Step-by-step explanation:

Why don't you just look for the whole area and deduct the non-shaded area?

Total

Sides:

a = 180 cm

b = 181 cm

c = 19 cm

Angles:

A = 83.9744 °

B = 90 °

C = 6.02558 °

Other:

P = 380 cm

s = 190 cm

K = 1710 cm^2

r = 9 cm

R = 90.5 cm

________________________

Non shaded area:

Answer:

Sides:

a = 40 cm

b = 41 cm

c = 19 cm

Angles:

A = 73.519 °

B = 79.3849 °

C = 27.0961 °

Other:

P = 100 cm

s = 50 cm

K = 373.497 cm^2

r = 7.46994 cm

R = 20.8569 cm

where:

A = angle A

B = angle B

C = angle C

a = side a

b = side b

c = side c

P = perimeter

s = semi-perimeter

K = area

r = radius of inscribed circle

R = radius of circumscribed circle

Answer 2

Answer: Approximately 1336.50301206033 square cm

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Step-by-step explanation:

If we know the three side lengths of a triangle, then we can use Heron's formula to get the area

Heron's formula is

`A = \sqrt{S(S-a)(S-b)(S-c)`

with S being the semiperimeter, or half the perimeter, so
`S = (a+b+c)/(2)`. We add up all three sides and divide by 2.

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The smaller triangle has side lengths of a = 19, b = 40, c = 41. So we get a semiperimeter of S = (a+b+c)/2 = (19+40+41)/2 = 50

Plug this along with the a,b,c values to get an area of...

`A = √(S(S-a)(S-b)(S-c))\\\\A = √(50(50-19)(50-40)(50-41))\\\\A = √(139500)\\\\A \approx 373.496987939661\\\\`

which is approximate

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Do the same for the larger triangle as well

S = (a+b+c)/2 = (19+180+181)/2 = 190

`A = √(S(S-a)(S-b)(S-c))\\\\A = √(190(190-19)(190-180)(190-181))\\\\A = √(2924100)\\\\A = 1710\\\\`

Interestingly enough, we get an exact area value this time as opposed to some approximation.

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The difference between the two results is the area of the shaded region

1710 - 373.496987939661 = 1336.50301206033

This is approximate since the first result was approximate.