Directions Make sure to write all answers in complete senten

Directions: Make sure to write all answers in complete sentences. For the following figures, explain how to derive the formula for the area.

iPad 11:28 AM webassign.net 47% 5 of 7 10. Concave Kite - where di and d2 are the diagonals of the kite. id d2 11. Regular Heptagon - a is the altiude, s is the length of a side. A=-as

Solution

1. We know that the area of the triangle is

A = 1/2 x base x height

In the case of concave kite d₂ is the base if we divide it into 2 equal triangle then

A = 1/2 x d₂/2 x d₁ + 1/2 x d₂/2 x d₁

A = 1/2 x d₂ x d₁ = 1/2 d₁d₂

2. In the regular heptagon each side is s and it can be divided into 7 triangle of equal area according to property of regular heptagon

So,The area of one triangle is

A = 1/2 x a x s

Then the are of all triangle is

A = 7/2as