Question

the given net can be folded to form a square pyramid atop a cube. the net consists of 5 congruent squares and 4 congruent triangles. what is the surface area of the composite solid that can be formed by this net? 144 cm² 80 cm² 160 cm² 120 cm²

Explanation:

Step1: Calculate the area of a square

The formula for the area of a square is \(A = s^2\), where \(s = 4\) cm.

$$A_{square}=4\times4 = 16\mathrm{cm}^2$$

Step2: Calculate the total area of 5 squares

$$A_{total - squares}=5\times16=80\mathrm{cm}^2$$

Step3: Calculate the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\), where \(b = 4\) cm and \(h = 5\) cm.

$$A_{triangle}=\frac{1}{2}\times4\times5=10\mathrm{cm}^2$$

Step4: Calculate the total area of 4 triangles

$$A_{total - triangles}=4\times10 = 40\mathrm{cm}^2$$

Step5: Calculate the total surface area

$$A_{total}=A_{total - squares}+A_{total - triangles}=80 + 40=120\mathrm{cm}^2$$

Answer:

\(120\mathrm{cm}^2\)