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primary 6 | Maths
| Algebra
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Date Posted: 2 months ago
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Draw a diagonal across from the top left corner of Y to its bottom right corner. We get a parallelogram with interior angles of 135° and 45°. Do the same for X to get a longer parallelogram with the interior angles of the same values.
Since parallelograms's opposite sides are of equal lengths, then the diagonal of square X and Y also equals 11.75cm. These two squares are congruent/identical.
Half of this diagonal equals the height of each of the two triangles in the square.
Area of 2 squares = area of 4 triangles
= 4 x ½ x b x h
= 2 x b x h
= 2 x 11.75 x 11.75/2
= 11.75 x 11.75
= 138.0625
= 138.06 cm² (to 2 decimal places)
Alternatively, area of 2 squares
= 2 x ½ x diagonal x diagonal
= diagonal x diagonal
= 11.75 x 11.75 (gives same answer as above)
Since parallelograms's opposite sides are of equal lengths, then the diagonal of square X and Y also equals 11.75cm. These two squares are congruent/identical.
Half of this diagonal equals the height of each of the two triangles in the square.
Area of 2 squares = area of 4 triangles
= 4 x ½ x b x h
= 2 x b x h
= 2 x 11.75 x 11.75/2
= 11.75 x 11.75
= 138.0625
= 138.06 cm² (to 2 decimal places)
Alternatively, area of 2 squares
= 2 x ½ x diagonal x diagonal
= diagonal x diagonal
= 11.75 x 11.75 (gives same answer as above)
b) it should be noted that the diagonal of the squares X and Y are also the radii of the two respective quadrants. These quadrants are inscribed in their respective squares so the side lengths of the two bigger squares also equals the length of the diagonal, 11.75cm
Perimeter of shaded region = arc length of the semicircle + four side lengths of the bigger squares
= half the circumference of a full circle + four radii
= πr + 4r
= 3.14 x 11.75 + 4 x 11.75
= 83.895
= 83.90cm (to 2 decimal places)
Perimeter of shaded region = arc length of the semicircle + four side lengths of the bigger squares
= half the circumference of a full circle + four radii
= πr + 4r
= 3.14 x 11.75 + 4 x 11.75
= 83.895
= 83.90cm (to 2 decimal places)
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