a convex octagon inscribed in a circle has four consecutive sides of length 3 and 4 consecutive sides of length 2. find the area of the octagon if if you solve this question I will mark you as brainliest answer

13 + 12√2

Step-by-step explanation:

Not sure if there's an easier way, but here's my method:

Draw the radius lines from the center of the circle to each vertex of the octagon.  This will divide the octagon into 8 isosceles triangles, 4 big and 4 small.

Draw the height of one of the big triangles.  Define the angle between the height and the radius as A.  Similarly, draw the height of one of the small triangles.  Define the angle between the height and the radius as B.

Using trig, we can say:

sin A = 1.5 / r

sin B = 1 / r

The vertex angle of the large isosceles triangle is 2A, and the vertex angle of the small isosceles triangle is 2B.  Therefore:

4(2A) + 4(2B) = 360

A + B = 45

If we substitute into the first trig equation:

sin(45 − B) = 1.5 / r

sin 45 cos B − cos 45 sin B = 1.5 / r

1/√2 cos B − 1/√2 (1/r) = 1.5 / r

cos B − 1/r = 1.5√2 / r

cos B = (1 + 1.5√2) / r

If we substitute into the second trig equation:

sin(45 − A) = 1 / r

sin 45 cos A − cos 45 sin A = 1 / r

1/√2 cos A − 1/√2 (1.5/r) = 1 / r

cos A − 1.5/r = √2 / r

cos A = (1.5 + √2) / r

Using SAS area of a triangle, the area of the large triangle is:

Area = ½ r² sin(2A)

Area = ½ r² (2 sin A cos A)

Area = r² sin A cos A

Area = (r sin A) (r cos A)

Area = (1.5) (1.5 + √2)

Area = 2.25 + 1.5√2

Similarly, the area of a small triangle is:

Area = ½ r² sin(2B)

Area = ½ r² (2 sin B cos B)

Area = r² sin B cos B

Area = (r sin B) (r cos B)

Area = (1) (1 + 1.5√2)

Area = 1 + 1.5√2

So the total area is:

Area = 4(2.25 + 1.5√2) + 4(1 + 1.5√2)

Area = 9 + 6√2 + 4 + 6√2

Area = 13 + 12√2

gregory's graph is incorrect because it shows 2 inches of growth for each week when it should show 0.75 inches of growth each week.

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2