Example Question - composed shapes

Calculation of Total Surface Area for Composed Shapes

<p>First, identify the shapes involved: a cube and a pyramid.</p> <p>The surface area of the cube (without the base that connects to the pyramid): Surface area of 3 faces of 5x5 cm: $3 \times (5 \times 5) = 3 \times 25 = 75 \text{ cm}^2$</p> <p>The surface area of the pyramid (without the base): Area of 4 triangular faces.</p> <p>Area of one triangle: $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 6 = 15 \text{ cm}^2$</p> <p>Surface area of the pyramid: $4 \times 15 = 60 \text{ cm}^2$</p> <p>Total surface area of the combined shape: Surface area of cube + Surface area of pyramid: $75 + 60 = 135 \text{ cm}^2$</p>