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Mathematics

Grade9

Easy

Question

Find the surface area of the figure. Round your answer to the nearest hundredth. (Hint: use the Pythagorean theorem to find half of the side length of the square)

$696.96 {cm}^{2}$
541.44 cm²
348.48 cm²
$329.76 {cm}^{2}$

hint Hint:

The surface area of Pyramid = where p is the perimeter of the base , B is area of the base and l is the slant height of the pyramid.

The correct answer is: $696.96 space cm squared$

Given, the slant height of pyramid is l = 17 cm and the height of pyramid is 15 cm. $B y space P y t h a g o r e a n space t h e o r e m comma H a l f space o f space t h e space s i d e squared space plus space 15.4 squared space equals space 17 squared space rightwards double arrow space H a l f space o f space t h e space s i d e squared space equals left parenthesis 17 minus 15.4 right parenthesis left parenthesis 17 plus 15.4 right parenthesis H a l f space o f space t h e space s i d e squared space equals space 51.84 space rightwards double arrow H a l f space o f space t h e space s i d e space equals 7.2 S i d e space equals 14.4 space c m space B a s e space a r e a space equals space 14.4 space space x space space 14.4 space space equals space 207.36 space c m squared P e r i m e t e r space o f space b a s e space equals space 4 space x space space 14.4 space equals space 57.6 space c m S u r f a c e space a r e a space equals space B space plus space 1 half space cross times space P l S. A space equals space 207.36 space plus 1 half space left parenthesis 57.6 right parenthesis left parenthesis 17 right parenthesis space equals space 207.36 space plus space 489.6 equals space 696.96 space c m squared$
Therefore, the surface area of the given figure is $696.96 space cm squared$ .

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