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A pyramid of slant length 6cm stands on a square base 4cm by 4cm.find

a.)the total surface area
b.)the volume of pyramid to 1dp

the area is the square base, plus four triangles, each with base=4, height=6

V = 1/3 Bh
Draw a side view, and it should be clear that
h^2 = 6^2 - (4/2)^2

Did you know?

Did you know that the total surface area of a pyramid can be determined by finding the sum of the areas of its base and its triangular faces? In the case of a pyramid with a square base measuring 4cm by 4cm and a slant length of 6cm, the total surface area can be found by calculating the area of the base (16 square cm) and the areas of the four triangular faces (4.8 square cm each, totaling 19.2 square cm). Therefore, the total surface area is 16 cm² + 19.2 cm², which equals 35.2 cm². Furthermore, did you know that the volume of a pyramid can be calculated by multiplying the area of its base by its height and dividing the result by 3? Applying this formula to the pyramid mentioned above, the volume can be determined by first finding the area of the base (16 square cm) and then multiplying it by the height, which is the slant length divided by the square root of 2 (6 cm ÷ √2 ≈ 4.243 cm). Finally, dividing the result by 3 gives a volume of approximately 22.571 cubic cm, rounded to 1 decimal place.