Chapter 11: Q17. (page 431)

Find the area of each figure:
A rhombus with perimeter and one diagonal 30 .

Short Answer

Expert verified

The area of given figure is 240 square units.

Step by step solution

Step 1. Given information.

Perimeter $p = 68$ and one diagonal $d_{1} = 30$ .

Step 2. Analyze the given information.

As the all four sides are equal in length in rhombus.

Let common side be a and Perimeter is 68 ,

Then, we can say $a + a + a + a = 68$

$4 a = 68$

$a = 17$

Step 3. Find the other diagonal of rhombus.

We can use Pythagoras theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

$17^{2} = 15^{2} + x^{2}$

$x^{2} = 289 - 225$

$x^{2} = 64$

$x = 8$

So the other diagonal will be $8 + 8 = 16$

Step 4. Find the area of given figure.

Area of rhombus can be found using the formula

$A = \frac{1}{2} d_{1} d_{2}$

Where,

$d_{1}$ and $d_{2}$ are the diagonals of arhombus

$A = \frac{1}{2} d_{1} d_{2}$

$= \frac{1}{2} \times 30 \times 16$

$= 30 \times 8$

= 240 Square units.

Therefore, the area of given figure is240 square units.

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Find the area of each figure:
A rhombus with perimeter and one diagonal 30 .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Analyze the given information.

Step 3. Find the other diagonal of rhombus.

Step 4. Find the area of given figure.

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Find the area of each figure:A rhombus with perimeter and one diagonal 30 .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Analyze the given information.

Step 3. Find the other diagonal of rhombus.

Step 4. Find the area of given figure.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Decision Maths

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find the area of each figure:
A rhombus with perimeter and one diagonal 30 .