Question

已知正四棱锥底面正方形的边长为4 cm，高与斜高夹角为35°,则斜高为_________；侧面积为_________；全面积为_________.(单位：精确到0.01)

Answer 1

3.49 cm  27.92 cm²  43.92 cm²

解析:

如图，正四棱锥的高PO，斜高PE，底面边心距OE组成直角△POE.

∵OE=2 cm，∠OPE=35°,

∴斜高PE=≈3.49(cm),

∴S_正棱锥侧=ch′=×4×4×≈27.92(cm²),

S_正棱锥全=4²+27.92=43.92(cm²).