Surface Area

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2. Find the surface area of a square pyramid whose slant height is 20 cm, and whose base has side 12 cm.

Further Discussion:

The surface area of a pyramid is tge sum of the lateral area and the area of the base. Formula is : SA = LA + B

Given data:

• Height - 20 cm
• Base - 12 cm

Solution & Answer

Step 1: Find the lateral area

Since there are four(4) congruent lateral triangular faces, let's find the areas of the triangles using LA = 4 (½ × b × h)

[tex]\sf LA = 4 \: (½ \times \: b×h)[/tex]

[tex]\sf LA = 4 \: (0.5 × 12 cm × 20 cm)[/tex]

[tex]\sf LA = 4 \: (0.5 × 240 \: cm^2)[/tex]

[tex]\sf LA = 4 \: (120 \: cm^2)[/tex]

[tex]\sf LA= 480 \: cm^2[/tex]

Step 2: Find the base

[tex]\sf B = s^2[/tex]

[tex]\sf B = (12 \: cm)^2[/tex]

[tex]\sf B= 144 \: cm^2[/tex]

Step 3: Find the surface area

[tex]\sf SA = LA + B[/tex]

[tex]\sf SA= 480 \: cm^2 + 144 \: cm^2[/tex]

[tex]\sf SA= \boxed{\sf624 \: cm^2}[/tex]

Answer:

Hence, the surface area of the square pyramid is 624 cm².

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