A sign company is building a sign with the dimensions shown.

What is the area, in square feet, of the sign?

Since the top of the sign has a length of 10 feet, split into two equal sections, then each section of the top is 5 feet.

The height of the triangle can be found by using the Pythagorean Theorem on either the left or right triangle.

5² + b² = 13² {substituted 5 in for a leg and 13 in for the hypotenuse, into the Pythagorean Theorem}

25 + b² = 169 {evaluated exponents}

b² = 144 {subtracted 25 from each side}

b = 12 {took square root of each side}

10 x 12

------- = area {substituted 10 for base and 12 for height, of triangle, into area formula}

2

120

---- = area {multiplied 10 by 12}

2

The height of the triangle can be found by using the Pythagorean Theorem on either the left or right triangle.

**Pythagorean Theorem****a² + b² = c²**{sum of the squares of the legs is equal to the square of the hypotenuse}5² + b² = 13² {substituted 5 in for a leg and 13 in for the hypotenuse, into the Pythagorean Theorem}

25 + b² = 169 {evaluated exponents}

b² = 144 {subtracted 25 from each side}

b = 12 {took square root of each side}

**height of triangle is 12 ft****base x height**

------------- = area of a triangle

2------------- = area of a triangle

2

10 x 12

------- = area {substituted 10 for base and 12 for height, of triangle, into area formula}

2

120

---- = area {multiplied 10 by 12}

2

**area = 60 ft²****Ask Algebra House**