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Triangle $OGK$ is shown where $OG=22.3$ centimeters $\text{cm}$ , $GK=32.5\text{cm}$ , $OK=21.9\text{cm}$ . Height of the triangle is $15\text{cm}$ . What is the area of $\triangle OGK$ ? $\newline$ (A) $244.185\text{cm}^2$ $\newline$ (B) $243.75\text{cm}^2$ $\newline$ (C) $167.25\text{cm}^2$ $\newline$ (D) $OG=22.3$ $0$

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Division with decimal divisors

Full solution

Q. Triangle

OGK

is shown where

OG=22.3

centimeters

\text{cm}

,

GK=32.5\text{cm}

,

OK=21.9\text{cm}

. Height of the triangle is

15\text{cm}

. What is the area of

\triangle OGK

?

\newline

(A)

244.185\text{cm}^2

\newline

(B)

243.75\text{cm}^2

\newline

(C)

167.25\text{cm}^2

\newline

(D)

OG=22.3

0

Identify Base: To find the area of a triangle, we can use the formula: Area = $\frac{\text{base} \times \text{height}}{2}$ . In this case, we can consider one of the sides of the triangle as the base. Since the height is given, we can use either OG, GK, or OK as the base, but typically the base is the side perpendicular to the given height. However, we are not given which side the height corresponds to, so we will assume that the height is perpendicular to one of the sides given. Let's assume the base is GK, which is $32.5$ cm.
Calculate Area: Now we can calculate the area using the base GK and the given height of $15$ cm. The area $A$ is given by the formula $A = (\text{base} \times \text{height}) / 2$ . $A = (32.5\,\text{cm} \times 15\,\text{cm}) / 2$
Perform Multiplication: Perform the multiplication before dividing by $2$ . $\newline$ $A = \frac{487.5 \, \text{cm}^2}{2}$
Divide by $2$ : Now divide by $2$ to find the area. $\newline$ $A = 243.75 \, \text{cm}^2$

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