If the lengths of three sides of a triangle are known, then the following formula, known as Hero's (or Heron's) formula, is sometimes used: A=√√s(sa)(s - b)(s - c) where a, b, and c are the given lengths of the sides, and s = 0.5(a + b + c). Use this formula to find the area (correct to the nearest square foot). a = 7 ft, b = 9 ft, c = 11 ft ft2

An artist wants to make a small monument in the shape of a square base topped by a right triangle, as shown below. The square base will be adjacent to one leg of the triangle. The other leg of the triangle will measure 2 feet and the hypotenuse will be 5 feet. (a) Use the Pythagorean Theorem to find the length of a side of the square base. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the face of the square base.

In the figure, a square is inscribed in a circle. If each side of the square measures 42 in., find an expression for the exact area of the shaded region.

Find the length of DE if: a DF=13 and EF=5. b DE=12 and EF=63. Exercises 7-10