Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u₁ = 12 cm and u₂ = 15 cm. Prism height is twice base edge length.

Correct result:

V = 1728.84 cm³
S = 918 cm²

Solution:

u_{1} = 12 cm u_{2} = 15 cm (u_{1} / 2)^{2} + (u_{2} / 2)^{2} = a^{2} a = \sqrt{(u_{1} / 2)^{2} + (u_{2} / 2)^{2}} = \sqrt{(12 / 2)^{2} + (15 / 2)^{2}} ≐ 9.6047 cm S_{1} = \frac{u_{1} \cdot u_{2}}{2} = \frac{12 \cdot 15}{2} = 90 {cm}^{2} h = 2 \cdot a = 2 \cdot 9.6047 = 3 \sqrt{41} cm ≐ 19.2094 cm V = S_{1} \cdot h = 90 \cdot 19.2094 = 270 \sqrt{41} = 1728.84 {cm}^{3}

o = 4 \cdot a = 4 \cdot 9.6047 = 6 \sqrt{41} cm ≐ 38.4187 cm S_{2} = o \cdot h = 38.4187 \cdot 19.2094 = 738 {cm}^{2} S = 2 \cdot S_{1} + S_{2} = 2 \cdot 90 + 738 = 918 {cm}^{2}

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