What is a shape that has a 24cm2 area and a 26cm perimeter. The sides have to be 5,4 and 3cm long!!!
Plz somebody help !!!
How do you get a heptagon?!!!!!!!!!!!!!!!!!!!!!!!!!!! It has to be a quadrilateral
Well, if the sides are 5,4,4,4,3,3,3 you have the perimeter of 26 cm.
So, you can build a nearly regular heptagon and just squash it till it has area 24 cm^2.
Or, a trapezoid on the side of a rectangle might also do the trick.
Please answer! I'm desperate to know.
To find the shape that has a 24cm^2 area and a 26cm perimeter with sides measuring 5cm, 4cm, and 3cm, we can approach this problem step by step.
Step 1: Determine the possible configurations of those side lengths.
- Given that the sides are 5cm, 4cm, and 3cm long, let's see how we can arrange those side lengths to form a shape with a perimeter of 26cm.
- The two sides with lengths 5cm and 4cm are already greater than the remaining side length of 3cm. So, we can determine that the shape is either a triangle or a quadrilateral (a four-sided polygon).
Step 2: Calculate the perimeter of the shape.
- The perimeter of a triangle is the sum of its side lengths, while for a quadrilateral, it is the sum of all four side lengths.
- For a triangle with side lengths of 5cm, 4cm, and 3cm, the perimeter is 5 + 4 + 3 = 12cm.
- For a quadrilateral with side lengths of 5cm, 4cm, 3cm, and 3cm, the perimeter is 5 + 4 + 3 + 3 = 15cm.
- Since the given perimeter is 26cm, it is not possible to form a triangle with those side lengths.
Step 3: Calculate the area of the shape.
- Since the shape is a quadrilateral, we need to find its area.
- We can use the formula for the area of a quadrilateral when given its side lengths: A = sqrt((s - a)(s - b)(s - c)(s - d)), where s is the semiperimeter and a, b, c, and d are the side lengths.
- In this case, a, b, c, and d are 5cm, 4cm, 3cm, and 3cm.
- The semiperimeter (s) can be calculated as half of the perimeter: s = 26 / 2 = 13cm.
- Plugging the values into the formula, the area (A) is: A = sqrt((13 - 5)(13 - 4)(13 - 3)(13 - 3)) = sqrt(16 * 9 * 10 * 10) = sqrt(14400) = 120cm^2.
- However, this area does not match the given area of 24cm^2, so it is not possible to form a quadrilateral with those side lengths either.
Therefore, it is not possible to find a shape with those given side lengths (5cm, 4cm, and 3cm) that has both a 24cm^2 area and a 26cm perimeter.