Given:
![m\angle ACD=45^\circ](https://img.qammunity.org/2022/formulas/mathematics/high-school/tgg6ngpczclexv3vjstxvr4jr1y9937hq9.png)
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)](https://img.qammunity.org/2022/formulas/mathematics/high-school/ukkqc91bk91zn9aawi7f6sztn52k5v3a68.png)
Where, a is the side length of the square.
Putting
in the above formula, we get
![d=10√(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/jp8bhznyoi7v1trhu85qf0t43t1f9yhf08.png)
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)](https://img.qammunity.org/2022/formulas/mathematics/high-school/z20v9nik5xemh1p8zyoh8oe72ddsnl19z3.png)
![BC=(10√(2))/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/t5jcegmnaug9mdvs4gn66tbga73q04oaje.png)
![BC=5√(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/skvx067imdkrshuf904xkw6gb3x23vw2fu.png)
In a right angle triangle,
![\tan \theta=(Perpendicular)/(Base)](https://img.qammunity.org/2022/formulas/mathematics/high-school/oviszp01ztar1sd4v8gvpgkffiw9v3snud.png)
In triangle ABC,
![\tan (45^\circ)=(AB)/(BC)](https://img.qammunity.org/2022/formulas/mathematics/high-school/9mktpepw30bwmj1xrxiax9gfybb7zwccem.png)
![1=(h)/(5√(2))](https://img.qammunity.org/2022/formulas/mathematics/high-school/eoahn43k1kq7ohqgmay3na2n9awdjyc71o.png)
![5√(2)=h](https://img.qammunity.org/2022/formulas/mathematics/high-school/3qtnr4r6b2dk8kpa7bhpnq66u9pu6m04mp.png)
![7.0710678=h](https://img.qammunity.org/2022/formulas/mathematics/high-school/zpbmu6yuurcwdc38h2shwo4n1glg28urv9.png)
Round the value to the nearest integer.
![h\approx 7](https://img.qammunity.org/2022/formulas/mathematics/high-school/1ggfbmbgqk515lizqqzvz277kptaxrl8nm.png)
The height of the pyramid is about 7 cm. Therefore, the correct option is A.