Question

use appropriate formulas to find (a) the perimeter and (b) the area of the figure (isosceles triangle). (a) the perimeter is (type an integer or a decimal.)

Explanation:

Step1: Recall perimeter formula for triangle

The perimeter $P$ of a triangle is $P = a + b + c$, where $a$, $b$, and $c$ are the side - lengths of the triangle. For an isosceles triangle, two sides have the same length. Here the side - lengths are $48.1$ mm, $48.1$ mm, and $28$ mm.
$P=48.1 + 48.1+28$

Step2: Calculate the sum

$P=(48.1 + 48.1)+28=96.2 + 28=124.2$ mm

Step3: Recall area formula for triangle

The area $A$ of a triangle is $A=\frac{1}{2}\times base\times height$. Here the base is $28$ mm and the height is $46$ mm.
$A=\frac{1}{2}\times28\times46$

Step4: Calculate the area

First, $\frac{1}{2}\times28 = 14$. Then $14\times46=644$ $mm^{2}$

Answer:

(a) The perimeter is $124.2$ mm
(b) The area is $644$ $mm^{2}$