Radius of inscribed circle to an isosceles triangle of base b = 10 and lateral side a = 12 is given by In triangle CDE we have: ∠DCE ∠CDE ∠CED = 180° In trangle ABC: ∠BCA ∠CAB ∠ABC = 180° Note that ∠ABC, ∠CBD and ∠DBE make a straight angle. Solutions to the equation: b = 10 and b = - 6ī is a length and therefore is positive b = 10, h = b - 4 = 6Ī = √ (h 2 (b/2) 2) = √ (36 25) = √61ĪBC is an isosceles triangle and therefore Substitute h by b - 4 in the formula for A Pythagora's theorem used in the right triangle CC'B (see figure at top) to writeĪ 2 = (b/2) 2 h 2 = √ ( 5 2 4 2) = √41 Use formula of area of isosceles triangle to write Use formula of area of isosceles triangle What is the area of an isosceles triangle of lateral side 2 units that is similar to another isosceles triangle of lateral side 10 units and base 12 units?Īpply Pythagora's theorem to the right triangle CC'B (see figure at top) to write Find the size of angle CED.įind the area of the circle inscribed to an isosceles triangle of base 10 units and lateral side 12 units.įind the ratio of the radii of the circumscribed and inscribed circles to an isosceles triangle of base b units and lateral side a units such that a = 2 b.įind the lateral side and base of an isosceles triangle whose height ( perpendicular to the base ) is 16 cm and the radius of its circumscribed circle is 9 cm. Find the size of angle BDE.ĪBC and CDE are isosceles triangles. What is the lateral side of an isosceles triangle such that its height h ( perpendicular to its base b) is 4 cm shorter than its base b and its area is 30 cm 2 ?ĪBC and BCD are isosceles triangles. What is the lateral side of an isosceles triangle with area 20 unit 2 and base 10 units? What is the base of an isosceles triangle with lateral side a = 5 cm and area 6 cm 2 ? What is the area of an isosceles triangle with base b of 8 cm and lateral a side 5 cm? The relationship between the lateral side \( a \), the based \( b \) of the isosceles triangle, its area A, height h, inscribed and circumscribed radii r and R respectively are give by: Problems on isosceles triangles are presented along with their detailed solutions.Īn Isosceles triangle has two equal sides with the angles opposite to them equal. Triangle, Right Triangle, Isosceles Triangle, IR Triangle, Quadrilateral, Rectangle, Golden Rectangle, Rhombus, Parallelogram, Half Square Kite, Right Kite, Kite, Right Trapezoid, Isosceles Trapezoid, Tri-equilateral Trapezoid, Trapezoid, Obtuse Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Concave Quadrilateral, Crossed Rectangle, Antiparallelogram, House-Shape, Symmetric Pentagon, Diagonally Bisected Octagon, Cut Rectangle, Concave Pentagon, Concave Regular Pentagon, Stretched Pentagon, Straight Bisected Octagon, Stretched Hexagon, Symmetric Hexagon, Parallelogon, Concave Hexagon, Arrow-Hexagon, Rectangular Hexagon, L-Shape, Sharp Kink, T-Shape, Square Heptagon, Truncated Square, Stretched Octagon, Frame, Open Frame, Grid, Cross, X-Shape, H-Shape, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Oktagram, Star of Lakshmi, Double Star Polygon, Polygram, PolygonĬircle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Circular Central Segment, Round Corner, Circular Corner, Circle Tangent Arrow, Drop Shape, Crescent, Pointed Oval, Two Circles, Lancet Arch, Knoll, Annulus, Annulus Sector, Curved Rectangle, Rounded Polygon, Rounded Rectangle, Ellipse, Semi-Ellipse, Elliptical Segment, Elliptical Sector, Elliptical Ring, Stadium, Spiral, Log.Problems on Isosceles Triangles with Detailed Solutions 1D Line, Circular Arc, Parabola, Helix, Koch Curve 2D Regular Polygons:Įquilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, Hexadecagon, N-gon, Polygon Ring
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