Question in image

Question

Answer 1

No problem - use right triangles!

Draw a line from the top vertex to the center - this the radius of the shape and the hypotenuse of a right triangle.

What's the area of that triangle? 1/2 B h = 1/2 * 6 * 4 = 12.

How many of those triangles make up the shape? Ten - two per side.

12 * 10 = 120.

Answer 2

it's a Pentagon, 5 sided regular polygon with each side = 8 cm

area = (a^2/4)sqr(25+10sqr5)

a=8, plug it into the formula

(8^2/4)sqr(25+10sqr5)

= 16sqr(25+10sqr5)

=about 110.11 cm^2

save some time doing the calculations and just go on line to a Pentagon area calculator, plug in the side and out pops the solution, voila tada. or if you do the calculations yourself, use the online calculator to check your answer. it says about 110.11 cm^2

Answer 3

area = 1/2 * apothem * perimeter

apothem is 6 cm

we have a regular pentagon with 5 sides all equal to 8 cm

perimeter = 5 * 8 cm = 40 cm

area = 1/2 * 6 cm * 40 cm = 120 cm^2