Math Problem Statement

Use the shape below to answer the following questions: a) Use a ruler and by calculation, to measure the dimensions of the shape above to the nearest mm. Show dimensions on the diagram. b) Use your dimensions to calculate the perimeter of the shape. c) Use your dimensions to calculate the area of the shape above, to 2 decimal places.

Solution

In the image you uploaded, we have a geometrical shape that resembles a combination of basic shapes: a rectangle, a quarter circle, and a triangle.

Here's a step-by-step approach to solve the given questions:

a) Measure and record dimensions (using a ruler)

  1. Measure the length of the rectangular part.
  2. Measure the width of the rectangular part.
  3. Measure the radius of the quarter-circle (which is part of the shape).
  4. Measure the height and base of the triangular part.

You will need a ruler to measure the dimensions from the diagram. Once you have those, write down the dimensions.

b) Calculate the perimeter

The perimeter would be the sum of all the outer boundaries of the shape. Since this shape is composed of a rectangle, a quarter-circle, and a triangle, we can calculate the perimeter as follows:

  • Rectangle: Add two sides.
  • Quarter-circle: The curved part of the quarter circle will be 14×2π×radius\frac{1}{4} \times 2\pi \times \text{radius}.
  • Triangle: Add the sides (if possible, use Pythagoras theorem for the slanted side if needed).

c) Calculate the area

The total area will be the sum of the areas of:

  • Rectangle: length×width\text{length} \times \text{width}.
  • Quarter-circle: 14πr2\frac{1}{4} \pi r^2.
  • Triangle: 12×base×height\frac{1}{2} \times \text{base} \times \text{height}.

Once you have these, sum up all the areas to find the total area of the shape.

Could you measure the dimensions using a ruler? Then we can proceed with calculations. Let me know if you'd like more guidance with the measurements!

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter
Area Calculation

Formulas

Perimeter of rectangle = 2 × (length + width)
Perimeter of quarter circle = (1/4) × 2πr
Area of rectangle = length × width
Area of quarter circle = (1/4) × πr^2
Area of triangle = (1/2) × base × height

Theorems

Pythagoras Theorem (for calculating the slanted side of the triangle if needed)

Suitable Grade Level

Grades 6-8