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Shape and Space

Shape and Space. Triangles. terms. Tri angle - A 3-sided polygon (a flat shape with straight sides) Square ( spanish ) - A 4-sided flat shape with straight sides where: all sides have equal length, and every angle is a right angle (90°)

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Shape and Space

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  1. Shape and Space Triangles

  2. terms • Triangle - A 3-sided polygon (a flat shape with straight sides) • Square (spanish) - A 4-sided flat shape with straight sides where: all sides have equal length, and every angle is a right angle (90°) • Perpendicular┴ - at an angle of 90° to a given line, plane, or surface • Base - The surface that a solid object stands on, or the bottom line of a shape such as a triangle or rectangle. • Height - The vertical distance from top to bottom • Right angle - An angle which is equal to 90°, one quarter of a full revolution.

  3. PERIMETER example 1 A = 2 B = 5 C = 5 Perimeter = ? a b 12 c The perimeter of a triangle is the measure around the triangle = a + b + c

  4. PERIMETER Check 1 A = 5 B = 5 C = 5 Perimeter = ? Check 2 A = 5 B = 10 C = 10 Perimeter = ? a b c The perimeter of a triangle is the measure around the triangle = a + b + c

  5. AREA Formula! 1/2bh = ½ x base x height example B = 10 H = 7 ½ x 10 x 7 = ? .5 x 10 x 7 = ? h .5 x 70 b = 35 To find the area of a triangle: The (h) height = the perpendicular distance from the opposite vertex to the (b) base

  6. Area of a right-angled triangle 1 2 What proportion of this rectangle has been shaded? 4 cm ☐ 8 cm What is the shape of the shaded part? What is the area of this right-angled triangle? Area of the triangle = × 8 × 4 = 4 × 4 = 16 cm2

  7. Area of a right-angled triangle Area of a triangle = × base × height 1 1 = bh 2 2 We can use a formula to find the area of a right-angled triangle: height, h base, b

  8. Area of a right-angled triangle Area = × base × height 1 1 2 2 = × 8 × 6 Calculate the area of this right-angled triangle. To work out the area of this triangle we only need the length of the base and the height. 8 cm 6 cm 10 cm We can ignore the third length opposite the right angle. = 24 cm2

  9. Area of a triangle 1 2 What proportion of this rectangle has been shaded? 4 cm 8 cm Drawing a line here might help. What is the area of this triangle? Area of the triangle = × 8 × 4 = 4 × 4 = 16 cm2

  10. Area of a triangle Area of a triangle = × base × perpendicular height perpendicular height 1 1 base 2 2 Area of a triangle = bh The area of any triangle can be found using the formula: Or using letter symbols,

  11. The area of a triangle b b h h h b Any side of the triangle can be taken as the base, as long as the height is perpendicular to it:

  12. Area of a triangle Area of a triangle = bh = × 7 × 6 1 1 2 2 What is the area of this triangle? 6 cm 7 cm = 21 cm2

  13. Area of a triangle

  14. The area of a triangle

  15. area = ½ ( 3 )( 6 ) = 9 square units area = ½ ( h )( b ) area = ½ ( 4 )( 7 ) = 14 square units area = ½ ( 5 )( 9 ) = 22 ½ square units

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