How to find the length of the diagonal of a pentagon - Math

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What is the length of a diagonal of a pentagon with side length of 20 centimeters (to the nearest tenth)?

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Let be the length fo a diagonal.

One interior angle of a pentagon measures

A diagonal of this pentagon, along with two sides, forms an isosceles triangle with sides 20, 20 and ; the side of length is opposite the angle of measure , and each side of length 20 is opposite an angle of measure .

The Law of Sines helps us to determine :

$$\frac{d $}{sin;108^{\circ}$$}=\frac{20 $}{sin;36^{\circ}$$}$

$d=\frac{20\cdot $sin;108^{\circ}$$ $}{sin;36^{\circ}$}\approx$\frac{20\cdot 0.9511 }{0.5878}$\approx 32.4$

In the pentagon below, the length of is one-third that of . Find the length of diagonal .

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Start by using the Pythagorean theorem to find the length of .

Since is one-third the length of , we know that the length of must be $3$\sqrt{340}$$ .

Now, notice that the pentagon is made up of one rectangle and two right triangles.

Focus on rectangle . We can find the length of by adding together the lengths of and .

$\text{AD}$=$\sqrt{324}$+3$\sqrt{324}$=4$\sqrt{324}$

Since we are working with a rectangle, we know that . Thus, we can use the Pythagorean Theorem again to find the length of .

Make sure to round to two places after the decimal.

Find the length of the diagonal of the following pentagon:

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Use the Pythagorean Theorem to find the length of the diagonal:

$(2\ $m)^2$+(2.75\ $m)^2$ = $C^2$$

$C\approx 3.4\ m$

Find the length of the diagonal of the following pentagon:

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Use the Pythagorean Theorem to find the length of the diagonal:

$(3\ $m)^2$+(3\ $m)^2$$=C^2$$

$C=3$\sqrt{2}$\ m$

What is the length of a diagonal of a pentagon with side length of 20 centimeters (to the nearest tenth)?

Tap to see back →

Let be the length fo a diagonal.

One interior angle of a pentagon measures

A diagonal of this pentagon, along with two sides, forms an isosceles triangle with sides 20, 20 and ; the side of length is opposite the angle of measure , and each side of length 20 is opposite an angle of measure .

The Law of Sines helps us to determine :

$$\frac{d $}{sin;108^{\circ}$$}=\frac{20 $}{sin;36^{\circ}$$}$

$d=\frac{20\cdot $sin;108^{\circ}$$ $}{sin;36^{\circ}$}\approx$\frac{20\cdot 0.9511 }{0.5878}$\approx 32.4$

In the pentagon below, the length of is one-third that of . Find the length of diagonal .

Tap to see back →

Start by using the Pythagorean theorem to find the length of .

Since is one-third the length of , we know that the length of must be $3$\sqrt{340}$$ .

Now, notice that the pentagon is made up of one rectangle and two right triangles.

Focus on rectangle . We can find the length of by adding together the lengths of and .

$\text{AD}$=$\sqrt{324}$+3$\sqrt{324}$=4$\sqrt{324}$

Since we are working with a rectangle, we know that . Thus, we can use the Pythagorean Theorem again to find the length of .

Make sure to round to two places after the decimal.

Find the length of the diagonal of the following pentagon:

Tap to see back →

Use the Pythagorean Theorem to find the length of the diagonal:

$(2\ $m)^2$+(2.75\ $m)^2$ = $C^2$$

$C\approx 3.4\ m$

Find the length of the diagonal of the following pentagon:

Tap to see back →

Use the Pythagorean Theorem to find the length of the diagonal:

$(3\ $m)^2$+(3\ $m)^2$$=C^2$$

$C=3$\sqrt{2}$\ m$

What is the length of a diagonal of a pentagon with side length of 20 centimeters (to the nearest tenth)?

Tap to see back →

Let be the length fo a diagonal.

One interior angle of a pentagon measures

A diagonal of this pentagon, along with two sides, forms an isosceles triangle with sides 20, 20 and ; the side of length is opposite the angle of measure , and each side of length 20 is opposite an angle of measure .

The Law of Sines helps us to determine :

$$\frac{d $}{sin;108^{\circ}$$}=\frac{20 $}{sin;36^{\circ}$$}$

$d=\frac{20\cdot $sin;108^{\circ}$$ $}{sin;36^{\circ}$}\approx$\frac{20\cdot 0.9511 }{0.5878}$\approx 32.4$

In the pentagon below, the length of is one-third that of . Find the length of diagonal .

Tap to see back →

Start by using the Pythagorean theorem to find the length of .

Since is one-third the length of , we know that the length of must be $3$\sqrt{340}$$ .

Now, notice that the pentagon is made up of one rectangle and two right triangles.

Focus on rectangle . We can find the length of by adding together the lengths of and .

$\text{AD}$=$\sqrt{324}$+3$\sqrt{324}$=4$\sqrt{324}$

Since we are working with a rectangle, we know that . Thus, we can use the Pythagorean Theorem again to find the length of .

Make sure to round to two places after the decimal.

Find the length of the diagonal of the following pentagon:

Tap to see back →

Use the Pythagorean Theorem to find the length of the diagonal:

$(2\ $m)^2$+(2.75\ $m)^2$ = $C^2$$

$C\approx 3.4\ m$

Find the length of the diagonal of the following pentagon:

Tap to see back →

Use the Pythagorean Theorem to find the length of the diagonal:

$(3\ $m)^2$+(3\ $m)^2$$=C^2$$

$C=3$\sqrt{2}$\ m$

What is the length of a diagonal of a pentagon with side length of 20 centimeters (to the nearest tenth)?

Tap to see back →

Let be the length fo a diagonal.

One interior angle of a pentagon measures

A diagonal of this pentagon, along with two sides, forms an isosceles triangle with sides 20, 20 and ; the side of length is opposite the angle of measure , and each side of length 20 is opposite an angle of measure .

The Law of Sines helps us to determine :

$$\frac{d $}{sin;108^{\circ}$$}=\frac{20 $}{sin;36^{\circ}$$}$

$d=\frac{20\cdot $sin;108^{\circ}$$ $}{sin;36^{\circ}$}\approx$\frac{20\cdot 0.9511 }{0.5878}$\approx 32.4$

In the pentagon below, the length of is one-third that of . Find the length of diagonal .

Tap to see back →

Start by using the Pythagorean theorem to find the length of .

Since is one-third the length of , we know that the length of must be $3$\sqrt{340}$$ .

Now, notice that the pentagon is made up of one rectangle and two right triangles.

Focus on rectangle . We can find the length of by adding together the lengths of and .

$\text{AD}$=$\sqrt{324}$+3$\sqrt{324}$=4$\sqrt{324}$

Since we are working with a rectangle, we know that . Thus, we can use the Pythagorean Theorem again to find the length of .

Make sure to round to two places after the decimal.

Find the length of the diagonal of the following pentagon:

Tap to see back →

Use the Pythagorean Theorem to find the length of the diagonal:

$(2\ $m)^2$+(2.75\ $m)^2$ = $C^2$$

$C\approx 3.4\ m$

Find the length of the diagonal of the following pentagon:

Tap to see back →

Use the Pythagorean Theorem to find the length of the diagonal:

$(3\ $m)^2$+(3\ $m)^2$$=C^2$$

$C=3$\sqrt{2}$\ m$