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(Multistep) $\newline$ Score: $\newline$ $0/4$ $\newline$ Penalty: $1$ off $\newline$ Question $\newline$ Watch Video $\newline$ Show Examples $\newline$ In $\Delta GHI$ , $g=85$ inches, $h=79$ inches and $i=22$ inches. Find the area of $\Delta GHI$ to the nearest $10$ th of an square inch. $\newline$ Answer Attempt $2$ out of $\(2\)

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Convert between customary and metric systems

Full solution

Q. (Multistep)

\newline

Score:

\newline

0/4

\newline

Penalty:

1

off

\newline

Question

\newline

Watch Video

\newline

Show Examples

\newline

In

\Delta GHI

,

g=85

inches,

h=79

inches and

i=22

inches. Find the area of

\Delta GHI

to the nearest

10

th of an square inch.

\newline

Answer Attempt

2

out of $\(2\)

Calculate Semi-Perimeter: To find the area of a triangle when the lengths of all three sides are known, we can use Heron's formula. Heron's formula states that the area of a triangle with sides of lengths $a$ , $b$ , and $c$ is the square root of $s(s-a)(s-b)(s-c)$ , where $s$ is the semi-perimeter of the triangle. The semi-perimeter is half the sum of the lengths of the sides. $\newline$ First, we calculate the semi-perimeter ( $s$ ) of triangle GHI. $\newline$ $s = (g + h + i) / 2$ $\newline$ $s = (85 + 79 + 22) / 2$ $\newline$ $s = 186 / 2$ $\newline$ $s = 93$ inches
Apply Heron's Formula: Now that we have the semi-perimeter, we can apply Heron's formula to find the area $A$ of the triangle. $A = \sqrt{s(s - g)(s - h)(s - i)}$ $A = \sqrt{93(93 - 85)(93 - 79)(93 - 22)}$ $A = \sqrt{93(8)(14)(71)}$ $A = \sqrt{93 \times 8 \times 14 \times 71}$ $A = \sqrt{74856}$ $A \approx 273.6$ square inches
Round Area: We need to round the area to the nearest tenth of a square inch as per the question prompt. $\newline$ The area of triangle $GHI$ to the nearest tenth of a square inch is approximately $273.6$ square inches.

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