Questions: 그림의 A B C D 에 대하여 물음에 답하시오. 【유형1. 직각삼각형의 변의 길이 124. A B C D 의 둘레의 길이는? (1) 12+4√6 (2) 14+4√3 (3) 14+6√3 (4) 12+6√6 (5) 12+8√6 125. A B C D 의 넓이는? (1) 10+4√3 (2) 12+4√6 (3) 12+8√3 (4) 10+8√6 (5) 24+16√3

Transcript text: 그림의 $\square A B C D$ 에 대하여 물음에 답하시오. 【유형1. 직각삼각형의 변의 길이 124. $A B C D$ 의 둘레의 길이는? (1) $12+4 \sqrt{6}$ (2) $14+4 \sqrt{3}$ (3) $14+6 \sqrt{3}$ (4) $12+6 \sqrt{6}$ (5) $12+8 \sqrt{6}$ 125. $\square A B C D$ 의 넓이는? (1) $10+4 \sqrt{3}$ (2) $12+4 \sqrt{6}$ (3) $12+8 \sqrt{3}$ (4) $10+8 \sqrt{6}$ (5) $24+16 \sqrt{3}$

Solution

Solution Steps

Step 1: Identify the given information

The quadrilateral $ABCD$ has angles $ \angle DAB = 45^\circ $ and $ \angle BCD = 30^\circ $.
$BC = 8$.

Step 2: Calculate the lengths of $AB$ and $AD$

Since $ \angle DAB = 45^\circ $, triangle $ABD$ is a 45-45-90 triangle.
In a 45-45-90 triangle, the legs are equal, and the hypotenuse is $ \sqrt{2} $ times the length of each leg.
Let $AB = x$. Then $AD = x$ and $BD = x\sqrt{2}$.

Step 3: Calculate the length of $CD$

Since $ \angle BCD = 30^\circ $, triangle $BCD$ is a 30-60-90 triangle.
In a 30-60-90 triangle, the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is $ \sqrt{3} $ times the shorter leg.
Given $BC = 8$, the hypotenuse $BD = 8\sqrt{3}$.

Final Answer

The perimeter of $ABCD$ is $12 + 8\sqrt{6}$.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!