Question

PLEASE HELP NEED THIS DONE ASAP

Answer 1

Answer:

The area of rhombus PQRS is 120 m.

Step-by-step explanation:

Consider the rhombus PQRS.

All the sides of a rhombus are equal.

Hence, PQ = QR = RS = SP = 13 m

The diagonals PR and QS bisect each other.

Let the point at of intersection of the two diagonals be denoted by X.

Consider the triangle QXR.

QR = 13 m

XR = 12 m

The triangle QXR is a right angled triangle.

Using the Pythagorean theorem compute the length of QX as follows:

QR² = XR² + QX²

QX² = QR² - XR²

       = 13² - 12²

       = 25

 QX = √25

       = 5 m

The measure of the two diagonals are:

PR = 2 × XR = 2 × 12 = 24 m

QS = 2 × QX = 2 × 5 = 10 m

The area of a rhombus is:

$\text{Area}=\frac{1}{2}\times d_{1}\times d_{2}$

Compute the area of rhombus PQRS as follows:

$\text{Area}=\frac{1}{2}\times PR\times QS$

        $=\frac{1}{2}\times 24\times 10\\\\=120$

Thus, the area of rhombus PQRS is 120 m.