# the total surface area of a rectangular wooden block with square base 6048 sq.cm. if the area of its base is 1296 sq cm, find its height.

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Expert Answers

baxthum8 | Certified Educator

The total surface area of a rectangular prism is found by: 2(lw+lh+wh)=SA where l represents the length, w is the width, and h represents height.

Since we know the Base is a square that means that the length and width are equal values. Therefore to find each length and width, take the square root of 1296.

Length and Width both = `sqrt(1296)=36`

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Therefore substituting these values in for the formula for surface area, solve for "h" to find the height.

SA = `2(36*36+36h+36h)`

`6048 = 2(1296+72h)`

`6048=2592+144h`

`-2592 = -2592`

`3456 = 144h`

`(3456)/(144)=(144h)/(144)`

`24=h`

`Therefore, the height of the wooden block is 24 centimeters.`

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