Answered

Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

different sizes of regular pentagons are used in a stained glass window.each small pentagon has side lengths of 4 inches and an area of 27.5 square inches.each large pentagon has a side lengths of 8 inches.what is the area of each large pentagon?

Sagot :

RedRicin
The goal is to find the area of a pentagon with side length 8.

We can find the area of a pentagon very easily by splitting it up into 10 congruent right triangles with the apothem as the height. The base of one of these triangles would be 4. The base angle would be 54 degrees, because it's half of the angle of a regular pentagon.

Using trig we find that the height of this triangle/apothem of the pentagon is equal to 4tan(54 degrees), which is about 5.506.

The area of a triangle is bh/2, so...4*5.506/2 = 11.011 in².
Times 10 triangles is 110.11 in².

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.