Write the Word or Phrase That Best Completes Each Statement $72 ^ { \circ }$

question 95

Essay

Write the word or phrase that best completes each statement or answers the question.
-Penrose tiles are formed from a rhombus WXYZ with sides of length 1 and interior angles $72 ^ { \circ }$ and $108 ^ { \circ }$ . (Refer to the illustration.) $A$ point $O$ is chosen on the diagonal 1 unit from $Y$ . Line segments $O X$ and $O Z$ are drawn to the o vertices. The two resulting tiles are called a kite (figure $\mathrm { OXYZ }$ ) and a dart (figure $\mathrm { OXWZ }$ ). Find the area of the kit and the dart tile, correct to the nearest $0.01$ .

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Definitions:

Actual Authority

The specific powers that a principal explicitly grants to an agent in the context of an agency relationship.

Manifested

The demonstration or display of the existence or presence of something through observable evidence.

Nondelegable Duty

A legal principle that refers to obligations that cannot be transferred to another party and must be performed by the one originally obligated.

Subagent

An agent appointed by another agent to perform tasks or services on behalf of the original agent's client.