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= $AD \times CD$

Other useful links

AMC-AIME Program at Cheenta

Related

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= $AD \times CD$

Other useful links

AMC-AIME Program at Cheenta

Related

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