Question

find the surface area of the prism using the net. find the area of the triangular bases. triangular bases: ? cm² side rectangles: ? cm² total surface area: ? cm² hint: a = b × h ÷ 2 (with a net diagram showing a triangular prism net: triangles with base 7 cm, height 6 cm; rectangles with dimensions 7 cm × 12 cm, 7 cm × 12 cm, 7 cm × 12 cm)

Explanation:

Step1: Calculate area of one triangular base

The formula for the area of a triangle is \( A = \frac{b \times h}{2} \). Here, the base \( b = 7 \) cm and height \( h = 6 \) cm. So, area of one triangle is \( \frac{7 \times 6}{2} = 21 \) \( cm^2 \).

Step2: Calculate area of two triangular bases

Since there are two triangular bases, multiply the area of one by 2. So, \( 21 \times 2 = 42 \) \( cm^2 \).

Step3: Calculate area of side rectangles

There are three rectangles, each with dimensions \( 7 \) cm (width) and \( 12 \) cm (height). The area of one rectangle is \( 7 \times 12 = 84 \) \( cm^2 \). For three rectangles, it's \( 84 \times 3 = 252 \) \( cm^2 \).

Step4: Calculate total surface area

Add the area of triangular bases and side rectangles. So, \( 42 + 252 = 294 \) \( cm^2 \).

Answer:

• Triangular bases: \( 42 \) \( cm^2 \)
• Side rectangles: \( 252 \) \( cm^2 \)
• Total surface area: \( 294 \) \( cm^2 \)