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AMC 8 2020 Problem 18 | Area Problem

Try this beautiful Problem based on area from AMC 8 2020.

Probability Problem - AMC 8 2020 Problem 18


Rectangle A B C D is inscribed in a semicircle with diameter \overline{F E}, as shown in the figure. Let D A=16, and let F D=A E=9. What is the area of A B C D ?

  • 240
  • 248
  • 256
  • 264
  • 272

Key Concepts


Area

Semi circle

Symmetry

Suggested Book | Source | Answer


AMC 8 2020 Problem 13

240

Try with Hints


Try to find the diameter of the semicircle. So the diameter will be,

The diameter of the semicircle is 9+16+9=34, so O C=17. By symmetry, O is the midpoint of AD,So, AO=OD=\frac{16}{2}=8.

Now, apply Pythagorean Theorem to find CD,

SO the area of ABCD will be=AD \times CD

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Try this beautiful Problem based on area from AMC 8 2020.

Probability Problem - AMC 8 2020 Problem 18


Rectangle A B C D is inscribed in a semicircle with diameter \overline{F E}, as shown in the figure. Let D A=16, and let F D=A E=9. What is the area of A B C D ?

  • 240
  • 248
  • 256
  • 264
  • 272

Key Concepts


Area

Semi circle

Symmetry

Suggested Book | Source | Answer


AMC 8 2020 Problem 13

240

Try with Hints


Try to find the diameter of the semicircle. So the diameter will be,

The diameter of the semicircle is 9+16+9=34, so O C=17. By symmetry, O is the midpoint of AD,So, AO=OD=\frac{16}{2}=8.

Now, apply Pythagorean Theorem to find CD,

SO the area of ABCD will be=AD \times CD

Subscribe to Cheenta at Youtube


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