The triangle shown in the diagram is a right angled triangle. The height is 7 ft while the base is unknown, but a portion of it is 4ft. The area of the triangle is given as;
Area = 1/2 base * height (or bh/2) where b is the base and h is the height)
Looking at the bigger triangle (there is a smaller one right inside the main triangle), the base can be calculated by using the Pythagoras' theorem which states that,
AC^2 = AB^2 + BC^2
Where AC is the longest side/hypotenuse (13 ft), AB is one of the other legs (7 ft) and BC is the base (unknown)
The formula can now be re-written as follows;
13^2 = 7^2 + BC^2
169 = 49 + BC^2
Subtract 49 from both sides of the equation
120 = BC^2
Add the square root sign to both sides of the equation (to eliminate the squared on the right hand side)
BC = 10.9544...
BC is approximately 11 ft
Having calculated the base to be 11 ft (approximately), the area can now be derived as follows;
Area of triangle = 1/2 base * height
Area = 1/2 (11 * 7)
Area = 1/2 (77)
Area = 38.5 ft