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

The formula for the area of a triangle is \(A = \frac{1}{2}bh\).
For the triangles with base \(10\) cm and height \(17.3\) cm: \(A_1=\frac{1}{2}\times10\times17.3 = 86.5\) \(cm^2\)
For the triangles with base \(15\) cm and height \(16.4\) cm: \(A_2=\frac{1}{2}\times15\times16.4 = 123\) \(cm^2\)
For the triangles with base \(10\) cm and height \(24.4\) cm: \(A_3=\frac{1}{2}\times10\times24.4 = 122\) \(cm^2\)
For the triangles with base \(15\) cm and height \(23.8\) cm: \(A_4=\frac{1}{2}\times15\times23.8 = 178.5\) \(cm^2\)

Step2: Calculate the total surface area

Since there are \(2\) of each type of triangular face in the composite figure (because two pyramids are joined), the total surface area \(S\) is:

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Answer:

\(1,020\ cm^2\)