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:
[tex]\text{Area}=\frac{1}{2}\times d_{1}\times d_{2}[/tex]
Compute the area of rhombus PQRS as follows:
[tex]\text{Area}=\frac{1}{2}\times PR\times QS[/tex]
[tex]=\frac{1}{2}\times 24\times 10\\\\=120[/tex]
Thus, the area of rhombus PQRS is 120 m.
