Equilateral pentagon of δ can be seen from the figure: Simplifying, δ is obtained as function of α and β: The remaining angles of the pentagon can be found geometrically: The remaining angles of the orange and blue triangles are readily found by noting that two angles of an isosceles triangle are equal while all three angles sum to 180°. Then formula_7 and the two remaining angles of the green triangle can be found from four equations stating that the sum of the angles of the pentagon is 540°, the sum of the angles of the green triangle is 180°, the angle
The Pentagon was planned accordingly as an irregular pentagon. Concerned that the new building could obstruct the view of Washington, D.C., from Arlington Cemetery, President Roosevelt ended up selecting the Hoover Airport site instead. The building retained its pentagonal layout because a major redesign at that stage would have been costly, and Roosevelt liked the design. Freed of the constraints of the asymmetric Arlington Farms site, it was modified into a regular pentagon which resembled the fortifications of the gunpowder age. On July 28, Congress authorized funding for a new Department of War building in Arlington, which would house the entire department