What is the surface area of the pyramid?
2 answers:
Answer:
166 square units
Step-by-step explanation:
Let’s find the area of the shapes that in the net.
First, we can see two of the triangles have a base of 2 and a height of 13. The formula for surface area of a triangle is bh÷2. (13x2)÷2=13. Since there are two triangles, we multiply 13 by 2 and get <u><em>26</em></u>.
Second, we can see two of the triangles have a base of 10 and a height of 12. (10x12)÷2=<u>60.</u> Since there are two triangles, we multiply 60 by 2 and get <u>120</u>.
Third, we can see a rectangle has a base of 10 and a height of 2. The formula for surface area of a rectangle is bh. 10x2=<u>20</u>.
Last, we add up all the areas:
20+120+26=166.
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Answer:
(1) D.Angle C is congruent to to Angle F. (2) C. SSS. (3) C. cannot be congruent to.
Step-by-step explanation:
1)
From the given figure it is noticed that
According to SAS postulate, if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then both triangles are congruent.
The included angles of congruent sides are angle C and angle G.
So, condition "Angle C is congruent to to Angle F" will prove that the ∆ABC and ∆EFG are congruent by the SAS criterion.
2)
If
According to SSS postulate, if all three sides in one triangle are congruent to the corresponding sides in the other.
Since two corresponding sides are congruent but third sides of triangles are not congruent, therefore SSS criterion for congruence is violated.
3)
Since two corresponding sides are congruent but third sides of triangles are not congruent, therefore the included angle of congruent sides are different.
Therefore angle C and angle F cannot be congruent to each other.
Let . Then
for all
, so
is strictly increasing. As
,
, so
is bounded above by 1. This is to say,
and the integral of converges over the same domain, so this integral must also converge by comparison.
We have, by setting ,