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What is the height of the pyramid ???

Answers:
A: 7cm
B: 5cm
C: 14 cm
D: 10 cm

What is the height of the pyramid ??? Answers: A: 7cm B: 5cm C: 14 cm D: 10 cm-example-1

1 Answer

4 votes

Given:


m\angle ACD=45^\circ

Point B is the center of the base.

Each side of the base = 10 cm

To find:

The height of the pyramid.

Solution:

It is given that the measure of each side of the base is 10 cm. It means the base is square. The length of the diagonal of a square is:


d=a√(2)

Where, a is the side length of the square.

Putting
a=10 in the above formula, we get


d=10√(2)

It is given that point B is the center of the base. It means point B bisect each diagonal of a base. So,


BC=(d)/(2)


BC=(10√(2))/(2)


BC=5√(2)

In a right angle triangle,


\tan \theta=(Perpendicular)/(Base)

In triangle ABC,


\tan (45^\circ)=(AB)/(BC)


1=(h)/(5√(2))


5√(2)=h


7.0710678=h

Round the value to the nearest integer.


h\approx 7

The height of the pyramid is about 7 cm. Therefore, the correct option is A.

User Dacort
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