Question

in $delta klm$, $k = 50$ cm, $l = 78$ cm and $m = 52$ cm. find the area of $delta klm$ to the nearest 10th of a square centimeter.

Explanation:

Step1: Calculate semi - perimeter

Let \(a = 50\), \(b = 78\), \(c = 52\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{50+78 + 52}{2}=\frac{180}{2}=90\) cm.

Step2: Apply Heron's formula

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}\). Substitute \(s = 90\), \(a = 50\), \(b = 78\), \(c = 52\) into the formula:

$$
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Rounding to the nearest tenth, \(A\approx1281.3\) \(cm^{2}\).

Answer:

\(1281.3\) \(cm^{2}\)