Question

two rectangular pyramids were joined at their bases to form the composite figure. what is the surface area of the figure? 1,325 cm² 1,020 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 \(24.4\) cm: \(A_1=\frac{1}{2}\times10\times24.4 = 122\) \(cm^2\)
For the triangles with base \(15\) cm and height \(23.8\) cm: \(A_2=\frac{1}{2}\times15\times23.8= 178.5\) \(cm^2\)
For the triangles with base \(10\) cm and height \(17.3\) cm: \(A_3=\frac{1}{2}\times10\times17.3 = 86.5\) \(cm^2\)
For the triangles with base \(15\) cm and height \(16.4\) cm: \(A_4=\frac{1}{2}\times15\times16.4 = 123\) \(cm^2\)

Step2: Sum up the areas of all triangular faces

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

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Answer:

\(1,020\space cm^2\)