Question

two rectangular pyramids were joined at their bases to form the composite figure. what is the surface area of the figure? 1,020 cm² 1,325 cm² 1,175 cm² 2,050 cm²

Explanation:

Step1: Calculate the area of each triangular face

• For the triangle with base \(10\) cm and slant height \(17.3\) cm:

The area of a triangle is \(A=\frac{1}{2}\times base\times height\). So, \(A_1 = \frac{1}{2}\times10\times17.3=86.5\) \(cm^{2}\)

• For the triangle with base \(15\) cm and slant height \(16.4\) cm:

\(A_2=\frac{1}{2}\times15\times16.4 = 123\) \(cm^{2}\)

• For the triangle with base \(10\) cm and slant height \(24.4\) cm:

\(A_3=\frac{1}{2}\times10\times24.4 = 122\) \(cm^{2}\)

• For the triangle with base \(15\) cm and slant height \(23.8\) cm:

\(A_4=\frac{1}{2}\times15\times23.8=178.5\) \(cm^{2}\)

Step2: Calculate the total surface area

Since the figure is made up of \(8\) triangular faces (4 pairs of congruent triangles), the total surface area \(S = 2\times(A_1 + A_2+A_3 + A_4)\)

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Answer:

\(1020\ cm^{2}\)