Find the perimeter of a regular octagon with an apothem of 6 feet and an area of 120 square feet
2 answers:
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You're very close. However, the less steep line should go through (4,7) and not some point slightly above that location. Also, the shaded region should be above both dashed lines at the same time. So you won't include the portion that I've marked in blue (see attached). Other than that, it looks great.
Answer:
Step-by-step explanation:
Consider triangles AMP and ADC. In these triangles,
- angle A is the common angle, so
by reflexive property;
- angles AMP and ADC are congruent as corresponding angles when two parallel lines MP and CD are cut by transversal AD.
Hence, triangles AMP and ADC are similar by AA similarity theorem.
Similar triangles have proportional corresponding sides, thus
so
Consider triangles ACB and PCN. In these triangles,
- angle C is the common angle, so
by reflexive property;
- angles ABC and PCN are congruent as corresponding angles when two parallel lines PN and AB are cut by transversal BC.
Hence, triangles ACB and PCN are similar by AA similarity theorem.
Similar triangles have proportional corresponding sides, thus
so
