Geometry Answers

A telephone Booth 210cm tall casts a shadow 600cm long.at the same time, a nearby fire hydrant casts a shadow 240cm long.find the height of the fire hydrant.

Calculate the area of rectangle 4.83m long and 3.58m wide

calculate the area of a circular disc 0.86m in diameter. (π=3.142)

Y is the midpoint of XZ and XZ = 20, what are the lengths of XY and YZ?

7. If a cube has an edge equal to the diagonal of another cube, find the ratio of their volumes.
8. The area of a circle circumscribing an equilateral triangle is 254.47 cm2, what is the area of the triangle?
9. The sides of an isosceles triangle are 10 and 16 m. (base). What is the length of the equal sides of a similar triangle if
the base is 10m?
10. If the radius of a circle is r, what is the apothem of an equilateral triangle inscribed in the circle?

1. The angle of a sector is 30° and the radius is 20 cm. What is the area of the sector in sq.cm.?
2. Find the area of the segment of a circle whose diameter is 20 cm and the central angle measures 70°
3. A square is inscribed in a circle whose area is 144π, determine the perimeter of the square.
A circle has an area equal to 25π cm2. Its diameter AB coincides with one of the sides of a triangle ACB whose vertex
C lies on the circle. Triangle ACB has an area equal to 15 cm2. What is the area of the portion of the circle which is outside the triangle in cm2?
5. Find the edge of a cube if its surface area is numerically equal to its volume
6. The base of a rectangular solid is 4 m long and 3 m wide. Find the volume of the solid if its diagonal is √41 m.

The base of the right prism is an equilateral triangle. The area of the base
is 1,560 cm2. If the altitude of the prism is 5 meters,
1. What is the base edge of the prism in cm?
2. What is the lateral area of the prism in m2?
3. What is the volume of the prism in m3?

The lateral edge of a square prism is 30 cm long and it is inclined at an
angle of 70 degrees with the base. If the volume of the prism is 1,500 cm3,
1. what is the base edge?
2. What is the lateral area of the prism?
3. What is the total area of the square prism?

Prove that the compass and straightedge construction for an angle bisector is valid.

Show that the triangle with vertices A(2,2), B(-1,1) and C (1,-1) is equilateral under the taxicab metric, but not under the euclidean metric