Final answer:
The lateral area of the regular pyramid with a square base area of 36 square cm and a slant height of 12 cm is 144 cm².
Step-by-step explanation:
To calculate the lateral area of a regular pyramid with a square base, you need to find the area of the four congruent triangles that make up the pyramid's sides. The formula for the area of a triangle is 1/2 × base × height. In this case, the height of each triangle is the slant height of the pyramid.
The area of the square base is given as 36 square cm, so each side of the square base (b) is √36 = 6 cm. The slant height (l) is given as 12 cm. Therefore, the area of each triangular side is:
1/2 × b × l = 1/2 × 6 cm × 12 cm = 36 cm²
Since there are four triangular sides, the total lateral area (LA) of the pyramid is:
LA = 4 × area of one triangle = 4 × 36 cm² = 144 cm²