SaiBook.us Geometry

Lesson Example Discussion Quiz: Class Homework

Example

Title: Quadrilaterals (Rhombus, Square)

Grade: 6-a Lesson: S2-L5

Explanation: The best way to understand geometry is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

The rhombus has a diagonal ratio of 8:6. If the small diagonal is 10 meters, what is the area of the rhombus?

Step 1a

Given that the small diagonal is 10 meters.

The ratio of the small diagonal to the large diagonal is 8 : 6.

$1a$

Explanation: Given that the small diagonal is 10 meters, the ratio of the small diagonal to the large diagonal is 4 : 3.

Step 1b

To find the area of a rhombus, you can use the formula: \$"Area" = ("d"1 \times "d"2) / 2\$.

Now, we can set up the following proportion: \$("Smaller diagonal") / ("Larger diagonal") = 8/6\$.

Explanation: Rhombus area formula: \$"Area" = ("d"1 \times "d"2) / 2\$.

Proportion: \$("Smaller diagonal") / ("Larger diagonal") = 8/6\$.

Step 1c

\$10 "meters" / ("Length of large diagonal") = 8/6\$

Length of large diagonal = \$(10 "meters" \times 6)/8\$

Length of large diagonal = 7.5 mtrs

Explanation: After solving the equation, we get the length of the large diagonal to be 7.5 meters.

Step 1d

Now that you have both diagonal lengths (d1 = 10 meters and d2 = 7.5 meters), you can calculate the area of the rhombus: Area = \$(d1 \times d2) / 2\$

Area = \$(10 "meters" \times 7.5 "meters") / 2\$

Area = 37.5 sq. mtrs

So, the area of the rhombus is 37.5 square meters.

Explanation: To calculate the area of a rhombus, use the formula: Area = \$(d1 \times d2) / 2\$.

For a rhombus with diagonal lengths of d1 = 10 meters and d2 = 7.5 meters, the area is 37.5 square meters.