In a right rectangular pyramid with base edges a=18 cm and b=10 cm the slant height towards a is k=13 cm while the slant height towards b is l=15 cm. Find: The surface area of the pyramid
To find the surface area of a right rectangular pyramid, we need to calculate the areas of its different components: the base, the lateral faces, and the total of those areas.
First, let's find the area of the base. We know that the base edges are given by a=18 cm and b=10 cm. Since it is a rectangle, the area of the base (A_base) is simply the product of its two sides:
A_base = a * b
Substituting the given values, we get:
A_base = 18 cm * 10 cm
A_base = 180 cm²
Next, let's find the areas of the lateral faces. Since it is a right rectangular pyramid, we have four lateral faces. The area of each lateral face is given by half the product of the base edge (either a or b) and the corresponding slant height.
The area of the lateral face towards a (A_lat_a) is given by:
A_lat_a = (1/2) * a * k
Substituting the given values, we get:
A_lat_a = (1/2) * 18 cm * 13 cm
A_lat_a = 117 cm²
Similarly, the area of the lateral face towards b (A_lat_b) is given by:
A_lat_b = (1/2) * b * l
Substituting the given values, we get:
A_lat_b = (1/2) * 10 cm * 15 cm
A_lat_b = 75 cm²
Now, to find the total surface area of the pyramid (A_total), we sum the area of the base and the areas of the four lateral faces:
A_total = A_base + A_lat_a + A_lat_a + A_lat_b + A_lat_b
Substituting the values we found:
A_total = 180 cm² + 117 cm² + 117 cm² + 75 cm² + 75 cm²
A_total = 564 cm²
Therefore, the surface area of the right rectangular pyramid is 564 cm².
You have two pairs of triangles, right?
You have the base and height, so just do the math.