Geometry Answers

A cuboid box of dimensions 20cm*10cm*8cm was made of cardboard.From the front face 2 circles of diameter 7 cm and a rectangle of 8 cm*2 cm were cut out.Find total surface area of cuboid?

A wooden box 2m long 68cm wide and 30cm high is packed with plastic blocks 10 cm long 8 cm broad and 5 cm wide.how many blocks are there in the box

Find the weight of an iron cylinder of height 20cm and radius of the base 10cm if 1 square centimetre of the iron weight 8 grams

ABCD is a trapezium in which AB is parallel to CD. O is mid point of BC. Through the point O, a line PQ parallel to AD has been dawn which intersects AB at Q and DC produced at P. Prove that ar(ABCD) = ar(AQPD).

The bade if a prism is a regular pentagon with sides 5 feet long and an apothem of 3.4 feet. If the prism us 6 feet tall, what is the volume of the prism?

surface area of a regular square pyramid with the slant height of 7 and base perimeter of 10

the maesure of one is four times the measure of the other? what is the answer for this question?

a bedroom with a wall area of 3528 square meters is to be covered by wallpaper. if the size of a roll wallpapers is 12 meters long and 42 meters wide, how many roll of wallpapers are needed to cover this area?

7^2+x^2=11^2

Claim Confirmation Collection of Calculations
A circle of radius R is inscribed in an equilateral triangle, all of whose sides are of length S.
A mathematician claims that the length of the line segment joining the center of the circle to any of the 3 triangle vertices is equal in length to the diameter of the circle. Your first task is to confirm that claim if it is true. Otherwise, you need to prove that the claim is not true.
Then you are to perform the appropriate calculations to determine:
The area of the circle in terms of S
The area of the triangle in terms of S
The area of the triangle in terms of R.
Note: If a appears in your work and/or in your solutions, just leave it that way. Do not convert to 1.732. Also, be sure to rationalize all denominators. And, of course, leave answers in terms of π when π appears.