Question

1. which of the following figures have an area of 20 square centimeters? choose all that apply. a. 8 cm 5 cm b. 5 cm 13 cm 8 cm 4 cm c. 5 cm 4 cm 12 cm d. 2 cm 3 cm 2 cm 5 cm 2 cm 2 cm 2 cm

Explanation:

Step1: Recall triangle area formula

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.
For option A: $b = 5$ cm, $h=8$ cm. Then $A=\frac{1}{2}\times5\times8= 20$ $cm^{2}$.

Step2: Calculate area for option B

For option B, the base $b=8 + 4=12$ cm and height $h = 5$ cm. So $A=\frac{1}{2}\times12\times5=30$ $cm^{2}$.

Step3: Recall parallelogram area formula

The area formula for a parallelogram is $A = bh$, where $b$ is the base and $h$ is the height. For option C, $b = 12$ cm and $h=4$ cm, so $A=12\times4 = 48$ $cm^{2}$.

Step4: Calculate area for option D

We can split option D into a rectangle and two right - angled triangles. The rectangle has length $l = 5$ cm and width $w=2$ cm, and its area $A_{rect}=5\times2 = 10$ $cm^{2}$. Each triangle has base $b = 2$ cm and height $h=2$ cm, and the area of each triangle is $A_{tri}=\frac{1}{2}\times2\times2 = 2$ $cm^{2}$. The total area of the two triangles is $2\times2=4$ $cm^{2}$. Another rectangle on the left has length $l = 2$ cm and width $w=(3 + 2)=5$ cm, and its area $A_{left - rect}=2\times5 = 10$ $cm^{2}$. The total area of the figure in option D is $10+4 + 10=24$ $cm^{2}$.

Answer:

A. A triangle with base 5 cm and height 8 cm has an area of 20 square centimeters.