Calculate Rectangle Area: 7-Unit Triangle and 10-Unit Height Problem

Question

Shown below is a rectangle and an isosceles right triangle.

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What is the area of the rectangle?

Video Solution

Solution Steps

00:00 Determine the area of the rectangle
00:06 Apply the Pythagorean theorem to the triangle ABC
00:12 The triangle is isosceles according to the given data
00:17 Substitute in the relevant values and solve to find AC
00:24 Extract the root
00:28 This is the length of side AC
00:35 Apply the formula for calculating the area of a rectangle
00:41 Side(AC) X by side(AE)
00:44 Substitute in the relevant values and proceed to solve
00:47 This is the solution

Step-by-Step Solution

To find the missing side, we use the Pythagorean theorem in the upper triangle.

Since the triangle is isosceles, we know that the length of both sides is 7.

Therefore, we apply PythagorasA2+B2=C2 A^2+B^2=C^2 72+72=49+49=98 7^2+7^2=49+49=98

Therefore, the area of the missing side is:98 \sqrt{98}

The area of a rectangle is the multiplication of the sides, therefore:

98×10=98.99≈99 \sqrt{98}\times10=98.99\approx99

Answer

≈99 \approx99

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Calculating the Area of a Rectangle Types of Triangles Area The Pythagorean Theorem Rectangle Equilateral triangle Isosceles triangle Acute triangle Obtuse Triangle Scalene triangle Identification of an Isosceles Triangle Areas of Polygons for 7th Grade Right Triangle Geometric shapes How do we calculate the area of complex shapes?

Question Types

Types of Triangles: Using Pythagoras' theorem Area of a Rectangle: Using Pythagoras' theorem