The quadrilateral pyramid

The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.

Correct result:

V = 10.24 dm³
S = 31.3831 dm²

Solution:

a = 24 cm \to dm = 24 / 10 dm = 2.4 dm b = 3.2 dm h = 0.4 m \to dm = 0.4 \cdot 10 dm = 4 dm S_{1} = a \cdot b = 2.4 \cdot 3.2 = \frac{192}{25} = 7.68 {dm}^{2} V = \frac{1}{3} \cdot S_{1} \cdot h = \frac{1}{3} \cdot 7.68 \cdot 4 = \frac{256}{25} = \frac{256}{25} {dm}^{3} = 10.24 {dm}^{3}

s_{2} = \sqrt{h^{2} + (a / 2)^{2}} = \sqrt{4^{2} + (2.4 / 2)^{2}} ≐ 4.1761 dm s_{3} = \sqrt{h^{2} + (b / 2)^{2}} = \sqrt{4^{2} + (3.2 / 2)^{2}} ≐ 4.3081 dm S_{2} = \frac{a \cdot s_{3}}{2} = \frac{2.4 \cdot 4.3081}{2} ≐ 5.1698 {dm}^{2} S_{3} = \frac{b \cdot s_{2}}{2} = \frac{3.2 \cdot 4.1761}{2} ≐ 6.6818 {dm}^{2} S = S_{1} + 2 \cdot S_{2} + 2 \cdot S_{3} = 7.68 + 2 \cdot 5.1698 + 2 \cdot 6.6818 = 31.3831 {dm}^{2}

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