a Corresponding parts of congruent solids are congruent. With this information and considering the Pythagorean Theorem, find the side lengths of the base.
We are asked to find the perimeter of the base of Pyramid A. Thus, we need to find the side lengths of the base. Note that corresponding parts of congruent solids are congruent. Because the length of one leg of the base of Pyramid B is 8 cm, so is the corresponding length of the leg of the base of Pyramid A.
Now we know two side lengths of the base of Pyramid A. Since the base is a right triangle, we can find the third length using the Pythagorean Theorem.
Finally, by adding the side lengths of the base together we can find its perimeter.
10+8+6=24
The perimeter of the base of Pyramid A is 24 cm.
b Next, we will find the area of the base of Pyramid B. Since the pyramids are congruent, their base areas are also congruent. Therefore, by finding the base area of Pyramid A we can find the base area of Pyramid B. Because the base is a right triangle, its area will be the half the product of its legs.
6* 8/2=24
The area of the base of Pyramid B is 24 cm^2.
c The volume of Pyramid B will be also the same as the volume of Pyramid A. The volume of a pyramid can be found using the following formula.
V=Bh/3
In this formula B is the base area and h is the height. We found that the base area is 24 cm^2 and we know that the height of the pyramid is 13 cm. Let's substitute these values into the formula and compute the volume.
