Geometry Answers

__24. A prismatoid has an upper base of 90%, a lower base of 2100%, an altitude of 100 cm, and a midsection of 120? What is its volume?

a) 7000 cm3
b) 11 500 cm3
c) 13 000 cm3
d) 17 500 cm3

25. Find the midsection of a frustum of a square pyramid if its lower base is 20 cm on a side, its upper base is 12 cm on a side, and the altitude of the frustum is 14 cm.

a)144 cm2
b) 240 cm2
c) 256 cm2
d) 400cm2

(with solution pls)

The base of a right prism is an equilateral triangle whose edges is 10cm each and its lateral edge is 80cm. _____

19. Find its volume in cm3.

a) 2,486.60
b) 3,464.10
c) 4,000.00
d) 8,000.00

20. Determine the total area of the prism in cm2.

a) 2,486.60
b) 3,464.10
c) 4,000.00
d) 8,000.00

(with solution pls)

1. A frustum of a regular hexagonal pyramid has an upper base edge of 5m and a lower base edge of 8.5m. Its lateral area is 160m2. Determine the slant height of the frustum.

a) 2.53 m
b) 3.95 m
c) 4.25 m
d) 15 m

(with solution pls)

State whether the following statements are true or false. Justify your answer with a brief explanation or with a counter-example.

(a) The curve x4 + y4 = 4a2xy is symmetric with respect to the origin.

(b) The direction cosines of the line x = — y, z=0 are 1/√2, -1/√2,0

(c) The section of 2x² + y²= 2 (1 — z²) by the plane x + 2 = 0 is a hyperbola.-

(d) The xy-plane intersects the sphere

x²+ y² + z² + 2x + 2y — z = 2 in a great circle.

(e) If the projection of a line segment AB on another line is the line segment CD, then

IABI = ICDI•

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

A square prism that has 5m base, 6m height,and 7 m width.
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 is1,500cm3,
1.what is the base edge?
2.What is the capacity of the trough in m3?
3.What is the wetted surface area of the trough if it is fully filled with water?

Prove that if two lines in same plane are cut by a transversal then the two lines are parallel if and only if a pair of interior angles on the same side of the transversal are supplementary.

prove a parallelogram is a square if and only if its diagnols are both congruent and perpendicular.

Prove that the base angles of an isoceles trapezoid are congruent.