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 Find the area of the rectangle
00:06 We'll use the Pythagorean theorem in triangle ABC
00:12 The triangle is isosceles according to the given data
00:17 We'll substitute appropriate values and solve to find AC
00:24 Extract the root
00:28 This is the length of side AC
00:35 We'll use the formula for calculating rectangle area
00:41 Side(AC) multiplied by side(AE)
00:44 We'll substitute appropriate values and solve
00:47 And this is the solution to the question

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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Related Subjects

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

Question Types

Types of Triangles: Using Pythagoras' theorem Area of a Rectangle: Using Pythagoras' theorem Using the Pythagorean Theorem: Using Pythagoras' theorem