Question

determine the surface area. 2.5m 80cm

Explanation:

Step1: Convert units

First, convert 80 cm to m. Since 1 m = 100 cm, then 80 cm=$0.8$m.

Step2: Calculate base - area

The base of the pyramid is a square. The area of the base $B$ (where side length $s = 0.8$m) is $B=s^{2}=0.8^{2}=0.64$m².

Step3: Calculate area of one triangular face

The area of a triangular face of a pyramid is $A_{triangle}=\frac{1}{2}×base×slant - height$. Here, the base of the triangular face is the side - length of the square base ($s = 0.8$m) and the slant - height $l = 2.5$m. So, $A_{triangle}=\frac{1}{2}×0.8×2.5 = 1$m².

Step4: Calculate total surface area

A square - based pyramid has 4 triangular faces and 1 square base. The total surface area $SA$ is $SA = B+4A_{triangle}$. Substitute $B = 0.64$m² and $A_{triangle}=1$m² into the formula: $SA=0.64 + 4×1=4.64$m².

Answer:

$4.64$m²