Example Question - rectangle geometry
Here are examples of questions we've helped users solve.
Calculating Area of a Rectangle
The image shows a sketch of a rectangle with its dimensions marked in units. The length of the rectangle is divided into two sections marked "2 units" and "2 units", indicating that the total length is 4 units. The width is not explicitly divided, but it is marked as "2 units". For Emma's Rectangle, we have the following information: Length: 2 units + 2 units = 4 units Width: 2 units To find the area of a rectangle, we multiply the length by the width: Area = Length × Width Area = 4 units × 2 units Calculating the area: Area = 8 square units So, Emma's Rectangle is 4 units long, 2 units wide, and has an area of 8 square units.
Calculating Area of Shaded Hexagon in a Rectangle
I see a geometric figure with a shaded area that you want to calculate. The overall figure appears to be a rectangle with a smaller, centered hexagon cut out, which is the shaded area. The dimensions given are for the rectangle and the side of the hexagon. To calculate the area of the shaded hexagon, we need to know the formula for the area of a regular hexagon, which depends on the length of its sides (s). The area (A) of a regular hexagon can be calculated using the following formula: \[ A = \frac{3\sqrt{3}}{2} \times s^2 \] Given that the side length (s) of the hexagon is 2 cm, we can substitute this value into the formula to find the area of the hexagon: \[ A = \frac{3\sqrt{3}}{2} \times 2^2 \] \[ A = \frac{3\sqrt{3}}{2} \times 4 \] \[ A = 6\sqrt{3} \text{ cm}^2 \] Now that we have the area of the hexagon, we can subtract it from the area of the larger rectangle to obtain the area of the shaded region. The area of the rectangle is found by multiplying its length and width: \[ \text{Area of rectangle} = \text{length} \times \text{width} \] \[ \text{Area of rectangle} = 10 \text{ cm} \times 6 \text{ cm} \] \[ \text{Area of rectangle} = 60 \text{ cm}^2 \] Now, subtract the area of the hexagon from the area of the rectangle: \[ \text{Area of shaded region} = \text{Area of rectangle} - \text{Area of hexagon} \] \[ \text{Area of shaded region} = 60 \text{ cm}^2 - 6\sqrt{3} \text{ cm}^2 \] This is the final expression for the area of the shaded region. If you need an approximate numerical answer, you can calculate the square root of 3 and multiply by 6, then subtract that result from 60. The square root of 3 is approximately 1.732, so: \[ \text{Area of shaded region} \approx 60 - 6 \times 1.732 \] \[ \text{Area of shaded region} \approx 60 - 10.392 \] \[ \text{Area of shaded region} \approx 49.608 \text{ cm}^2 \] Therefore, the approximate area of the shaded region is 49.608 square centimeters.
Finding Length of Line Segment in Rectangle
In the image, we have a rectangle PQRS with diagonals PR and QS that intersect at point H. You are asked to find the length of the line segment HS given that QS = 14. In a rectangle, the diagonals are equal in length and they bisect each other. This means that the diagonals are divided into two equal parts at their intersection point. Since QS = 14, and the diagonals bisect each other, QH = HS = QS / 2. Therefore, HS = 14 / 2 = 7. So the length of HS is 7. The correct answer is D) 7.
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