Use the following image to answer the questions below. the base is a regular pentagon and the vertex is directly above the center of the base: a. if you knew the dimensions of this solid, how would you calculate the surface area? b. how would you calculate the volume? c. how does the volume of this pentagonal pyramid compare to the volume of a prism with a congruent pentagonal base and a congruent height? d. what cross-sectional shapes, regular or irregular, could you get by cutting a plane through this figure? explain your answer.
a. The lateral area is the area of 5 congruent triangles. The strategy for computing their area will depend on the dimensions given. There are methods for computing triangle area based on side lengths, base length and height, coordinates of the points, and other dimensions. One straightforward way, given the appropriate dimensions is to multiply the slant height by the perimeter of the base, then divide that product by 2.
The base area is that of 5 congruent triangles. Again, their total area can be computed from half the product of the perimeter of the base and the apothem (height of the triangle).
The total surface area is the sum of lateral area and base area.
For example, given the apothem of the base (a) and the slant height of the side face (s), the total surface area (A) will be
... A = 5·a·tan(36°)·(a + s)
b. The volume is conventionally calculated as 1/3 of the product of the base area (B) and the height (h).
... V = (1/3)Bh
c. The volume of a prism with the same base area and height will be
... V = Bh
The volume of a pyramid is 1/3 of that.
d. A plane can intersect this pyramid to form a triangle, rectangle, trapezoid or other irregular quadrilateral, pentagon, or hexagon. The number of edges the cross-section has depends on the number of faces (including the base) the plane cuts. That number can be 3 through 6.
I'd say South Africa because there is Dutch in the sign and during that time they were ruled under British and Dutch at that time period.
I think the answer is 4. hieroglyphics invented by the Sumerians
Hope this helps :)
Just wanted to let you know that "Which of the following would probably want independence from Spain but not a complete social revolution?" is NOT a Mestizo. I would assume the answer would be "A peninsulare" due to the fact that they controlled the governments of the colonies and were born in Europe. So they'd want independence from another country, but would still want to remain with some power. The creoles would also be a decent answer because they are in a good spot and own a lot of land, but don't have any say in the government. The answer is not slaves because they of course would want a major change. Hope this helps!
1 - political independence from Europe
(mainly fom Spain and Portugal)
2 - the use of large-scale slavery
(for plantation of cane or cotton)
3 - a mestizo
(a child from a "white" person and "indogious" person)
4 - separation and independence from Spain
5 - the continuation of the caste system
6 - the many border disputes and wars
7 - The period of administrative freedom caused by the war gave leaders the opportunity to rebel for these rights.
8 - The United States hoped to benefit territorially from problems in Latin America.
Shape A can be split into two shapes as shown in the diagram below. One is a rectangle and the other is an isosceles triangle. The dimension of the rectangle is 80×180 but we do not know the base of the triangle.
Area of rectangle = 80×180 = 14400
Base of rectangle can be worked out using the Pythagoras theorem
the base of the triangle = 2×25 = 50
Area of rectangle = 1/2(base)(height) = 0.5×50×60 = 1950
Total area of shape A = 1950 + 14400 = 16350
Tax = 16350÷100 = $163.50
Total perimeter of shape A = 80+80+180+65+65 = 470
We split shape B into a parallelogram and a trapezium
Area of parallelogram = base × height = 250 × 30 = 7500
Area of trapezium = × =×
Total area = 5600 + 7500 = 13100
Tax = 13100÷100 = $131
Perimeter = 250+250+35+35+100+40+80 = 790
Shape C is an isosceles shape which allows us to split side bc into 100÷2=50. The diagram is shown in the third diagram.
Quadrilateral PODY = Quadrilaterla AXPO
Side CY =
Side PY = 50+38.1 = 88.1
Side DS = (rounded to whole number)
Side OP = 100-77=23
Area of PODY =
Area of DCY =
Area of DCPO = 5418.15-1905 = 3513.15
Area of ABCD = 3513.15×2 = 7026.3
Tax = 7026.3÷100 = $70.263
Perimeter = 117+117+107+107+100 = 548
Shape D can be split into a triangle and a trapezium as shown in the fourth diagram below
Area of triangle =
Area of trapezium =
Total area = 22500 + 160000 = 182500
Tax = 182500÷100 = $1825
Perimeter = 280+165+406+500+425 = 1776
Ray PL and ray PQ
Opposite rays always have the same endpoint in common. So opposite rays start with the same letter.
Opposite rays also lay on the same geometric line. This means they point in complete opposite directions. Gluing together two opposite rays forms a line that extends forever in both directions.
Ray PQ points in one direction while ray PL points in the opposite direction. These are opposite rays.
Saying "ray PQ" is different from saying "ray QP". The order matters. This is because the first letter tells you the endpoint while the second letter is where the ray is aimed at (and where it goes off forever).